# How to generate the reward signal in temporal difference (TD) learning algorithm?

With reference to the TD learning algorithm proposed by Sutton and Barto which is given by the equations:

\$\$V_i(t+1) = V_i (t)+ eta igg(lambda(t+1)+gamma igg[sum_{j}V_j(t)X_j(t+1)igg]-igg[sum_{j}V_j(t)X_j(t) igg] igg)alphaar{X}_i(t+1), ar{X}_i(t+1)=ar{X}_i(t)+deltaig(X_i(t)-ar{X}_i(t)ig)\$\$ I have the following doubts:

1. If I want to simulate the algorithm in a standalone environment then how do I generate the reward signal \$lambda(t+1)\$?
2. How is \$lambda(t+1)\$ related to the conditioning stimulus and the unconditioned stimulus?

For example, if I wanted to simulate the facilitation of a remote association by an intervening stimulus in the TD model as shown in the fig. below then will it suffice if I consider "lambda" to be a signal as represented by US ?

I have been able to design suitable CSA and CSB. However, when I use a \$lambda\$ as specified by US in the image, I don't get the result that is shown in the trials. What could possibly go wrong in the formulation of the reward?

The equations can be found in chapter 12 of the book by Sutton & Barto, 1990. The chapter is titled "Time-Derivative Models of Pavlovian Reinforcement".

Sutton, R. S., & Barto, A. G. (1990). Learning and computational neuroscience: foundations of adaptive networks. A/1 IT Press, Cambridge, MA, 497-437.

## TD(λ) in Delphi/Pascal (Temporal Difference Learning)

I have an artificial neural network which plays Tic-Tac-Toe - but it is not complete yet.

What I have yet:

• the reward array "R[t]" with integer values for every timestep or move "t" (1=player A wins, 0=draw, -1=player B wins)
• The input values are correctly propagated through the network.
• the formula for adjusting the weights:

What is missing:

• the TD learning: I still need a procedure which "backpropagates" the network's errors using the TD(λ) algorithm.

But I don't really understand this algorithm.

My approach so far .

The trace decay parameter λ should be "0.1" as distal states should not get that much of the reward.

The learning rate is "0.5" in both layers (input and hidden).

It's a case of delayed reward: The reward remains "0" until the game ends. Then the reward becomes "1" for the first player's win, "-1" for the second player's win or "0" in case of a draw.

My questions:

• How and when do you calculate the net's error (TD error)?
• How can you implement the "backpropagation" of the error?
• How are the weights adjusted using TD(λ)?

Thank you so much in advance :)

## Domain Selection for Reinforcement Learning

One way to imagine an autonomous reinforcement learning agent would be as a blind person attempting to navigate the world with only their ears and a white cane. Agents have small windows that allow them to perceive their environment, and those windows may not even be the most appropriate way for them to perceive what’s around them.

### Interested in reinforcement learning?

Automatically apply RL to simulation use cases (e.g. call centers, warehousing, etc.) using Pathmind.

(In fact, deciding which types of input and feedback your agent should pay attention to is a hard problem to solve. This is known as domain selection. Algorithms that are learning how to play video games can mostly ignore this problem, since the environment is man-made and strictly limited. Thus, video games provide the sterile environment of the lab, where ideas about reinforcement learning can be tested. Domain selection requires human decisions, usually based on knowledge or theories about the problem to be solved e.g. selecting the domain of input for an algorithm in a self-driving car might include choosing to include radar sensors in addition to cameras and GPS data.)

## Keywords

Sen Wang is an Associate Professor in the School of Software Engineering, Chongqing University, Chongqing, China. He received B.S., M.S., and Ph.D. degree in computer science in University of Science and Technology of China (USTC), Chinese Academy of Sciences (CAS) and Tsinghua University, China, in 2005, 2008 and 2014, respectively. His research interests include in-network caching, Information-centric Networking, Cloud Computing, Software Defined Networking and Network Functions Virtualization.

Jun Bi received the B.S., M.S., and Ph.D. degree in Computer Science from Tsinghua University, Beijing, China, from 1990 to 1999. From 2000 to 2003, he was a research scientist of Bell Labs Research Communication Science Division and Bell Labs Advanced Communication Technologies Center, New Jersey, USA. Currently he is a full professor and the director of Network Architecture & IPv6 Research Division, Institute for Network Sciences and Cyberspace of Tsinghua University, and a Ph.D. Supervisor with the Department of Computer Science, Tsinghua University. He is a Senior Member of the IEEE, ACM and a Distinguished Member of China Computer Federation. He served as chair of Asia Future Internet Forum Steering Group, chair of INFOCOM NOM workshop and ICNP CoolSDN workshop, and member of technical program committee of NFOCOM, ICNP, CoNEXT, SOSR, etc.

Jianping Wu is a professor of Computer Science and director of Network Research Center, Tsinghua University, Beijing, China. From 1994, he has been in charge of China Education and Re-search Network (CERNET) which is the largest academic network in the world as a director of both Network Center and Technical Board. He had served as chairman or program committee member for many international conferences, such as chairman of FORTE/PSTV’1999, and program committee member of INFOCOM’2002, ICNP’2001 and 2006, FORTE/PSTV’ 1995–2003 and TESTCOM’ 1995–2006 etc. His area of specialization includes high speed computer net-work, Internet and its applications, network protocol testing and formal method.

## Model-free prediction

Dynamic programming enables us to determine the state-value and action-value functions given the dynamics (model) of the system. It does this by mathematically using the Bellman equations and plugging in the dynamics (rewards and probabilities).

If the model (rewards and probabilities) of the system is not known a priori, we can empirically estimate the value functions for a given policy. We do this by taking actions according to the given policy, and taking note of the state transitions and rewards. By making enough number of trials, we are able to converge to the value functions for the given policy.

### Monte-Carlo learning

This applies to experiments which are run as episodes. Each episode terminates and next episode is independent of the current episode. As an example, when a board game is played, each new game constitutes a separate episode.

Given a policy, action is taken in each state according to the policy. For a state that is arrived at time , return for a particular run through the termination of the episode is calculated:

Here, is the reward obtained by taking action in the state at time .

Such returns are added for all the episodes during which the state is visited to obtain total return for the state:

And, number of episodes (or in an alternate method, number of visits??) that the state is visited is calculated.

Value of the state is estimated as mean return , since by law of large numbers as .

Note that running average return can calculated online (real-time) as the episodes are run instead of calculating it only after all episodes are completed as follows:

In practice in online learning scenario, rather than using for weighing the return from current episode, a constant factor with is used. This leads to the formulation:

What is the reasoning? Rather than the average over all episodes, returns from recent episodes is given more weight than returns from old episodes. Returns from episodes are given weights that exponentially decrease with time.

### Temporal-Difference (TD) learning

In contrast to Monte-Carlo learning, Temporal-Difference (TD) learning can learn the value function for non-episodic experiments.

In Monte-Carlo learning, we run through a complete episode, note the “real” return obtained through the end of the episode and accumulate these real returns to estimate the value of a state.

In TD learning, we do as follows:

1. we initialize the value for each state.
2. we run the experiment (according to the given policy) for a certain number of steps (not necessarily to the end of the episode or experiment). The number of steps we run the experiment is identified as -step TD (or TD(), for short) learning.
3. we note the reward obtained in these steps.
4. We then use the Bellman equation to estimate the return for the remaining of the experiment. This estimated return is . This estimated total return is called TD target.
5. We update similar to online Monte-Carlo learning except that here, we use estimated return rather than the “real” return. That is, we update using: . The quantity is called TD error.

How do we determine in TD() learning? We don’t. In what is called TD() learning, we use geometric weighting of estimated returns of all steps to obtain:

Exploitation and exploration concept is inherently linked to human nature, where we, as humans we prefer known compared to the unknown. For example, going to a restaurant, you can choose to go to your favorite restaurant since you already like the food there, but unless and until you try another restaurant you won’t know if there exists a better restaurant.

Exploitation is thus going or doing the same action, which gives the best value from a state (it is often called Greedy action), while exploration is to try out new activities which may give a better return in the long run even though the immediate reward may not be encouraging. In the above diagram, if the agent only considers immediate reward by following the red path to gain the maximum reward, it will later find the blue path that has a higher value even through immediate reward is lower. That’s why exploration is needed to make a better long term return.

## Conclusion

Timing and RL have for the most part been studied separately, giving rise to largely non-overlapping computational models. We have argued here, however, that these models do in fact share some important commonalities and reconciling them may provide a unified explanation of many behavioral and neural phenomena. While in this brief review we have only sketched such a synthesis, our goal is to plant the seeds for future theoretical unification.

One open question concerns how to reconcile the disparate theoretical ideas about time representation that were described in this paper. Our synthesis proposed a central role for a distributed elements representation of time such as the microstimuli of Ludvig et al. (2008). Could a representation deriving from the semi-Markov or pacemaker-accumulator models be used instead? This may be possible, but there are several reasons to prefer the microstimulus representation. First, microstimuli lend themselves naturally to the linear function approximation architecture that has been widely used in RL models of the basal ganglia. In contrast, the semi-Markov model requires additional computational machinery, and it is not obvious how to incorporate the pacemaker-accumulator model into RL theory. Second, the semi-Markov model accounts for the relationship between temporal precision and interval length at the expense of deviating from the normative RL framework. Third, as we noted earlier, pacemaker-accumulator models have a number of other weaknesses (see Staddon and Higa, 1999, 2006 Matell and Meck, 2004 Simen et al., 2013), such as lack of parsimony, implausible neurophysiological assumptions, and incorrect behavioral predictions. Nonetheless, it will be interesting to explore what aspects of these models can be successfully incorporated into the next generation of RL models.

### Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

## Reinforcement Learning Tutorial

If you are looking for a beginner’s or advanced level course in Reinforcement Learning, make sure that apart from a basic introduction, it includes a deep delving analysis of RL with an emphasis upon Q-Learning, Deep Q-Learning, and advanced concepts into Policy Gradients with Doom and Cartpole. You should choose a Reinforcement Learning tutorial that teaches you to create a framework and steps for formulating a Reinforcement problem and implementation of RL. You should also know about recent RL advancements. I suggest you visit Reinforcement Learning communities or communities, where the data science experts, professionals, and students share problems, discuss solutions, and answers to RL-related questions.

Machine learning or Reinforcement Learning is a method of data analysis that automates analytical model building. It is a branch of artificial intelligence based on the idea that systems can learn from data, identify patterns and make decisions with minimal human intervention.

Most industries working with large amounts of data have recognized the value of machine learning technology. By gleaning insights from this data – often in real time – organizations are able to work more efficiently or gain an advantage over competitors.

Data Analytics courses by Digital Vidya

Data Analytics represents a bigger picture of Machine learning. Just as Data Analytics has various categories based on the Data used, Machine Learning also expresses the way one machine learns a code or works in a supervised, unsupervised, semi-supervised and reinforcement manner.

To gain more knowledge about Reinforcement and its role in Data Analytics you may opt for online or classroom Certification Programs. If you are a programmer looking forward to a career in machine learning or data science, go for a Data Analytics course for more lucrative career options in Inductive Logic Programming. Digital Vidya offers advanced courses in Data Analytics. Industry-relevant curriculums, pragmatic market-ready approach, hands-on Capstone Project are some of the best reasons for choosing Digital Vidya.

A self-starter technical communicator, capable of working in an entrepreneurial environment producing all kinds of technical content including system manuals, product release notes, product user guides, tutorials, software installation guides, technical proposals, and white papers. Plus, an avid blogger and Social Media Marketing Enthusiast.

Date: 26th Jun, 2021 (Saturday)
Time: 10:30 AM - 11:30 AM (IST/GMT +5:30)

## Temporal-difference learning

The finding of a cue fERN indicated that participants evaluated intermediate states in terms of future reward. This result is consistent with a class of TD models in which credit is assigned based on immediate and future rewards. To evaluate whether the behavioral and ERP results reflected such an RL process, we examined the predictions of three RL algorithms: actor/critic (Barto, Sutton, & Anderson 1983), Q-learning (Watkins & Dayan, 1992), and SARSA (Rummery & Niranjan, 1994). Additionally, we considered variants of each algorithm with and without eligibility traces (Sutton & Barto, 1998).

### Models

#### Actor/critic

The actor/critic model (AC) learns a preference function, p(s,a), and a state-value function, V(s). The preference function, which corresponds to the actor, enables action selection. The state-value function, which corresponds to the critic, enables outcome evaluation. After each outcome, the critic computes the prediction error,

The temporal discount parameter, γ, controls how steeply future reward is discounted, and the critic treats future reward as the value of the next state. The critic uses prediction error to update the state-value function,

The learning rate parameter, α, controls how heavily recent outcomes are weighted. By using prediction error to adjust state values, the critic learns to predict the sum of the immediate reward, rt+1, and the discounted value of future reward, γ· V(st+1).

The actor also uses prediction error to update the preference function,

By using prediction error to adjust action preferences, the actor learns to select advantageous behaviors. The probability of selecting an action, π(s,a), is determined by the softmax decision rule,

The selection noise parameter, τ, controls the degree of randomness in choices. Decisions become stochastic as τ increases, and decisions become deterministic as τ decreases.

#### Q-learning

AC and Q-learning differ in two ways. First, Q-learning uses an action-value function, Q(s,a), to select actions and to evaluate outcomes. Second, Q-learning treats future reward as the value of the optimal action in state t+1,

The agent uses prediction error to update action values (Eq. 6), and the agent selects actions according to a softmax decision rule.

#### SARSA

Like Q-learning, SARSA uses an action-value function, Q(s,a), to select actions and to evaluate outcomes. Unlike Q-learning, however, SARSA treats future reward as the value of the actual action selected in state t+1,

The agent uses prediction error to update action values (Eq. 6), and the agent selects actions according to a softmax decision rule.

#### Eligibility traces

Although RL algorithms provide a solution to the temporal credit assignment problem, eligibility traces can greatly improve the efficiency of these algorithms (Sutton & Barto, 1998). Eligibility traces provide a temporary record of events such as visiting states or selecting actions, and they mark events as eligible for update. Researchers have applied eligibility traces to behavioral and neural models (Bogacz, McClure, Li, Cohen, & Montague 2007 Gureckis & Love, 2009 Pan, Schmidt, Wickens, & Hyland 2005). In these simulations, we took advantage of the fact that eligibility traces facilitate learning when delays separate actions and rewards (Sutton & Barto, 1998).

In AC, a state’s trace is incremented when the state is visited, and traces fade according to the decay parameter λ,

Prediction error is calculated in the conventional manner (Eq. 1), but the error signal is used to update all states according to their eligibility,

Separate traces are stored for state�tion pairs in order to update the preference function, p(s,a). Similarly, in Q-learning and SARSA, traces are stored for state�tion pairs in order to update the action-value function, Q(s, a).

## Footnotes

Author contributions: P.W.G. wrote the paper.

The author declares no conflict of interest.

This paper results from the Arthur M. Sackler Colloquium of the National Academy of Sciences, “Quantification of Behavior” held June 11–13, 2010, at the AAAS Building in Washington, DC. The complete program and audio files of most presentations are available on the NAS Web site at www.nasonline.org/quantification.

↵*It is important to acknowledge that there are alternative views of the function of these neurons. Berridge (53) has argued that dopamine neurons play a role closely related to the one described here that is referred to as incentive salience. Redgrave and Gurney (54) have argued that dopamine plays a central role in processes related to attention.

## TD(λ) in Delphi/Pascal (Temporal Difference Learning)

I have an artificial neural network which plays Tic-Tac-Toe - but it is not complete yet.

What I have yet:

• the reward array "R[t]" with integer values for every timestep or move "t" (1=player A wins, 0=draw, -1=player B wins)
• The input values are correctly propagated through the network.
• the formula for adjusting the weights:

What is missing:

• the TD learning: I still need a procedure which "backpropagates" the network's errors using the TD(λ) algorithm.

But I don't really understand this algorithm.

My approach so far .

The trace decay parameter λ should be "0.1" as distal states should not get that much of the reward.

The learning rate is "0.5" in both layers (input and hidden).

It's a case of delayed reward: The reward remains "0" until the game ends. Then the reward becomes "1" for the first player's win, "-1" for the second player's win or "0" in case of a draw.

My questions:

• How and when do you calculate the net's error (TD error)?
• How can you implement the "backpropagation" of the error?
• How are the weights adjusted using TD(λ)?

Thank you so much in advance :)

## Keywords

Sen Wang is an Associate Professor in the School of Software Engineering, Chongqing University, Chongqing, China. He received B.S., M.S., and Ph.D. degree in computer science in University of Science and Technology of China (USTC), Chinese Academy of Sciences (CAS) and Tsinghua University, China, in 2005, 2008 and 2014, respectively. His research interests include in-network caching, Information-centric Networking, Cloud Computing, Software Defined Networking and Network Functions Virtualization.

Jun Bi received the B.S., M.S., and Ph.D. degree in Computer Science from Tsinghua University, Beijing, China, from 1990 to 1999. From 2000 to 2003, he was a research scientist of Bell Labs Research Communication Science Division and Bell Labs Advanced Communication Technologies Center, New Jersey, USA. Currently he is a full professor and the director of Network Architecture & IPv6 Research Division, Institute for Network Sciences and Cyberspace of Tsinghua University, and a Ph.D. Supervisor with the Department of Computer Science, Tsinghua University. He is a Senior Member of the IEEE, ACM and a Distinguished Member of China Computer Federation. He served as chair of Asia Future Internet Forum Steering Group, chair of INFOCOM NOM workshop and ICNP CoolSDN workshop, and member of technical program committee of NFOCOM, ICNP, CoNEXT, SOSR, etc.

Jianping Wu is a professor of Computer Science and director of Network Research Center, Tsinghua University, Beijing, China. From 1994, he has been in charge of China Education and Re-search Network (CERNET) which is the largest academic network in the world as a director of both Network Center and Technical Board. He had served as chairman or program committee member for many international conferences, such as chairman of FORTE/PSTV’1999, and program committee member of INFOCOM’2002, ICNP’2001 and 2006, FORTE/PSTV’ 1995–2003 and TESTCOM’ 1995–2006 etc. His area of specialization includes high speed computer net-work, Internet and its applications, network protocol testing and formal method.

## Conclusion

Timing and RL have for the most part been studied separately, giving rise to largely non-overlapping computational models. We have argued here, however, that these models do in fact share some important commonalities and reconciling them may provide a unified explanation of many behavioral and neural phenomena. While in this brief review we have only sketched such a synthesis, our goal is to plant the seeds for future theoretical unification.

One open question concerns how to reconcile the disparate theoretical ideas about time representation that were described in this paper. Our synthesis proposed a central role for a distributed elements representation of time such as the microstimuli of Ludvig et al. (2008). Could a representation deriving from the semi-Markov or pacemaker-accumulator models be used instead? This may be possible, but there are several reasons to prefer the microstimulus representation. First, microstimuli lend themselves naturally to the linear function approximation architecture that has been widely used in RL models of the basal ganglia. In contrast, the semi-Markov model requires additional computational machinery, and it is not obvious how to incorporate the pacemaker-accumulator model into RL theory. Second, the semi-Markov model accounts for the relationship between temporal precision and interval length at the expense of deviating from the normative RL framework. Third, as we noted earlier, pacemaker-accumulator models have a number of other weaknesses (see Staddon and Higa, 1999, 2006 Matell and Meck, 2004 Simen et al., 2013), such as lack of parsimony, implausible neurophysiological assumptions, and incorrect behavioral predictions. Nonetheless, it will be interesting to explore what aspects of these models can be successfully incorporated into the next generation of RL models.

### Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Exploitation and exploration concept is inherently linked to human nature, where we, as humans we prefer known compared to the unknown. For example, going to a restaurant, you can choose to go to your favorite restaurant since you already like the food there, but unless and until you try another restaurant you won’t know if there exists a better restaurant.

Exploitation is thus going or doing the same action, which gives the best value from a state (it is often called Greedy action), while exploration is to try out new activities which may give a better return in the long run even though the immediate reward may not be encouraging. In the above diagram, if the agent only considers immediate reward by following the red path to gain the maximum reward, it will later find the blue path that has a higher value even through immediate reward is lower. That’s why exploration is needed to make a better long term return.

## Domain Selection for Reinforcement Learning

One way to imagine an autonomous reinforcement learning agent would be as a blind person attempting to navigate the world with only their ears and a white cane. Agents have small windows that allow them to perceive their environment, and those windows may not even be the most appropriate way for them to perceive what’s around them.

### Interested in reinforcement learning?

Automatically apply RL to simulation use cases (e.g. call centers, warehousing, etc.) using Pathmind.

(In fact, deciding which types of input and feedback your agent should pay attention to is a hard problem to solve. This is known as domain selection. Algorithms that are learning how to play video games can mostly ignore this problem, since the environment is man-made and strictly limited. Thus, video games provide the sterile environment of the lab, where ideas about reinforcement learning can be tested. Domain selection requires human decisions, usually based on knowledge or theories about the problem to be solved e.g. selecting the domain of input for an algorithm in a self-driving car might include choosing to include radar sensors in addition to cameras and GPS data.)

## Temporal-difference learning

The finding of a cue fERN indicated that participants evaluated intermediate states in terms of future reward. This result is consistent with a class of TD models in which credit is assigned based on immediate and future rewards. To evaluate whether the behavioral and ERP results reflected such an RL process, we examined the predictions of three RL algorithms: actor/critic (Barto, Sutton, & Anderson 1983), Q-learning (Watkins & Dayan, 1992), and SARSA (Rummery & Niranjan, 1994). Additionally, we considered variants of each algorithm with and without eligibility traces (Sutton & Barto, 1998).

### Models

#### Actor/critic

The actor/critic model (AC) learns a preference function, p(s,a), and a state-value function, V(s). The preference function, which corresponds to the actor, enables action selection. The state-value function, which corresponds to the critic, enables outcome evaluation. After each outcome, the critic computes the prediction error,

The temporal discount parameter, γ, controls how steeply future reward is discounted, and the critic treats future reward as the value of the next state. The critic uses prediction error to update the state-value function,

The learning rate parameter, α, controls how heavily recent outcomes are weighted. By using prediction error to adjust state values, the critic learns to predict the sum of the immediate reward, rt+1, and the discounted value of future reward, γ· V(st+1).

The actor also uses prediction error to update the preference function,

By using prediction error to adjust action preferences, the actor learns to select advantageous behaviors. The probability of selecting an action, π(s,a), is determined by the softmax decision rule,

The selection noise parameter, τ, controls the degree of randomness in choices. Decisions become stochastic as τ increases, and decisions become deterministic as τ decreases.

#### Q-learning

AC and Q-learning differ in two ways. First, Q-learning uses an action-value function, Q(s,a), to select actions and to evaluate outcomes. Second, Q-learning treats future reward as the value of the optimal action in state t+1,

The agent uses prediction error to update action values (Eq. 6), and the agent selects actions according to a softmax decision rule.

#### SARSA

Like Q-learning, SARSA uses an action-value function, Q(s,a), to select actions and to evaluate outcomes. Unlike Q-learning, however, SARSA treats future reward as the value of the actual action selected in state t+1,

The agent uses prediction error to update action values (Eq. 6), and the agent selects actions according to a softmax decision rule.

#### Eligibility traces

Although RL algorithms provide a solution to the temporal credit assignment problem, eligibility traces can greatly improve the efficiency of these algorithms (Sutton & Barto, 1998). Eligibility traces provide a temporary record of events such as visiting states or selecting actions, and they mark events as eligible for update. Researchers have applied eligibility traces to behavioral and neural models (Bogacz, McClure, Li, Cohen, & Montague 2007 Gureckis & Love, 2009 Pan, Schmidt, Wickens, & Hyland 2005). In these simulations, we took advantage of the fact that eligibility traces facilitate learning when delays separate actions and rewards (Sutton & Barto, 1998).

In AC, a state’s trace is incremented when the state is visited, and traces fade according to the decay parameter λ,

Prediction error is calculated in the conventional manner (Eq. 1), but the error signal is used to update all states according to their eligibility,

Separate traces are stored for state�tion pairs in order to update the preference function, p(s,a). Similarly, in Q-learning and SARSA, traces are stored for state�tion pairs in order to update the action-value function, Q(s, a).

## Footnotes

Author contributions: P.W.G. wrote the paper.

The author declares no conflict of interest.

This paper results from the Arthur M. Sackler Colloquium of the National Academy of Sciences, “Quantification of Behavior” held June 11–13, 2010, at the AAAS Building in Washington, DC. The complete program and audio files of most presentations are available on the NAS Web site at www.nasonline.org/quantification.

↵*It is important to acknowledge that there are alternative views of the function of these neurons. Berridge (53) has argued that dopamine neurons play a role closely related to the one described here that is referred to as incentive salience. Redgrave and Gurney (54) have argued that dopamine plays a central role in processes related to attention.

## Model-free prediction

Dynamic programming enables us to determine the state-value and action-value functions given the dynamics (model) of the system. It does this by mathematically using the Bellman equations and plugging in the dynamics (rewards and probabilities).

If the model (rewards and probabilities) of the system is not known a priori, we can empirically estimate the value functions for a given policy. We do this by taking actions according to the given policy, and taking note of the state transitions and rewards. By making enough number of trials, we are able to converge to the value functions for the given policy.

### Monte-Carlo learning

This applies to experiments which are run as episodes. Each episode terminates and next episode is independent of the current episode. As an example, when a board game is played, each new game constitutes a separate episode.

Given a policy, action is taken in each state according to the policy. For a state that is arrived at time , return for a particular run through the termination of the episode is calculated:

Here, is the reward obtained by taking action in the state at time .

Such returns are added for all the episodes during which the state is visited to obtain total return for the state:

And, number of episodes (or in an alternate method, number of visits??) that the state is visited is calculated.

Value of the state is estimated as mean return , since by law of large numbers as .

Note that running average return can calculated online (real-time) as the episodes are run instead of calculating it only after all episodes are completed as follows:

In practice in online learning scenario, rather than using for weighing the return from current episode, a constant factor with is used. This leads to the formulation:

What is the reasoning? Rather than the average over all episodes, returns from recent episodes is given more weight than returns from old episodes. Returns from episodes are given weights that exponentially decrease with time.

### Temporal-Difference (TD) learning

In contrast to Monte-Carlo learning, Temporal-Difference (TD) learning can learn the value function for non-episodic experiments.

In Monte-Carlo learning, we run through a complete episode, note the “real” return obtained through the end of the episode and accumulate these real returns to estimate the value of a state.

In TD learning, we do as follows:

1. we initialize the value for each state.
2. we run the experiment (according to the given policy) for a certain number of steps (not necessarily to the end of the episode or experiment). The number of steps we run the experiment is identified as -step TD (or TD(), for short) learning.
3. we note the reward obtained in these steps.
4. We then use the Bellman equation to estimate the return for the remaining of the experiment. This estimated return is . This estimated total return is called TD target.
5. We update similar to online Monte-Carlo learning except that here, we use estimated return rather than the “real” return. That is, we update using: . The quantity is called TD error.

How do we determine in TD() learning? We don’t. In what is called TD() learning, we use geometric weighting of estimated returns of all steps to obtain:

## Reinforcement Learning Tutorial

If you are looking for a beginner’s or advanced level course in Reinforcement Learning, make sure that apart from a basic introduction, it includes a deep delving analysis of RL with an emphasis upon Q-Learning, Deep Q-Learning, and advanced concepts into Policy Gradients with Doom and Cartpole. You should choose a Reinforcement Learning tutorial that teaches you to create a framework and steps for formulating a Reinforcement problem and implementation of RL. You should also know about recent RL advancements. I suggest you visit Reinforcement Learning communities or communities, where the data science experts, professionals, and students share problems, discuss solutions, and answers to RL-related questions.

Machine learning or Reinforcement Learning is a method of data analysis that automates analytical model building. It is a branch of artificial intelligence based on the idea that systems can learn from data, identify patterns and make decisions with minimal human intervention.

Most industries working with large amounts of data have recognized the value of machine learning technology. By gleaning insights from this data – often in real time – organizations are able to work more efficiently or gain an advantage over competitors.

Data Analytics courses by Digital Vidya

Data Analytics represents a bigger picture of Machine learning. Just as Data Analytics has various categories based on the Data used, Machine Learning also expresses the way one machine learns a code or works in a supervised, unsupervised, semi-supervised and reinforcement manner.

To gain more knowledge about Reinforcement and its role in Data Analytics you may opt for online or classroom Certification Programs. If you are a programmer looking forward to a career in machine learning or data science, go for a Data Analytics course for more lucrative career options in Inductive Logic Programming. Digital Vidya offers advanced courses in Data Analytics. Industry-relevant curriculums, pragmatic market-ready approach, hands-on Capstone Project are some of the best reasons for choosing Digital Vidya.

A self-starter technical communicator, capable of working in an entrepreneurial environment producing all kinds of technical content including system manuals, product release notes, product user guides, tutorials, software installation guides, technical proposals, and white papers. Plus, an avid blogger and Social Media Marketing Enthusiast.

Date: 26th Jun, 2021 (Saturday)
Time: 10:30 AM - 11:30 AM (IST/GMT +5:30)