Actor-critic algorithm: Difference between revisions

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{{Short description|Reinforcement learning algorithmalgorithms that combinescombine policy and value estimation}}

The '''actor-critic algorithm''' (AC) is a family of [[reinforcement learning]] (RL) algorithms that combine policy-based RL algorithms such as [[Policypolicy gradient method|policy gradient methods]]s, and value-based RL algorithms such as value iteration, [[Q-learning]], [[State–action–reward–state–action|SARSA]], and [[Temporal difference learning|TD learning]].<ref>{{Cite journal |lastlast1=Arulkumaran |firstfirst1=Kai |last2=Deisenroth |first2=Marc Peter |last3=Brundage |first3=Miles |last4=Bharath |first4=Anil Anthony |date=November 2017 |title=Deep Reinforcement Learning: A Brief Survey |url=http://ieeexplore.ieee.org/document/8103164/ |journal=IEEE Signal Processing Magazine |volume=34 |issue=6 |pages=26–38 |doi=10.1109/MSP.2017.2743240 |arxiv=1708.05866 |bibcode=2017ISPM...34...26A |issn=1053-5888}}</ref>

An AC algorithm consists of two main components: an "'''actor'''" that determines which actions to take according to a policy function, and a "'''critic'''" that evaluates those actions according to a value function.<ref>{{Cite journal |lastlast1=Konda |firstfirst1=Vijay |last2=Tsitsiklis |first2=John |date=1999 |title=Actor-Critic Algorithms |url=https://proceedings.neurips.cc/paper/1999/hash/6449f44a102fde848669bdd9eb6b76fa-Abstract.html |journal=Advances in Neural Information Processing Systems |publisher=MIT Press |volume=12}}</ref> Some AC algorithms are on-policy, some are off-policy. Some apply to either continuous or discrete action spaces. Some work in both cases.

== Overview ==

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=== Actor ===

The '''actor''' uses a policy function <math>\pi(a|s)</math>, while the critic estimates either the [[value function]] <math>V(s)</math>, the action-value Q-function <math>Q(s,a),

</math>, the advantage function <math>A(s,a)</math>, or any combination thereof.

The actor is a parameterized function <math>\pi_\theta</math>, where <math>\theta</math> are the parameters of the actor. The actor takes as argument the state of the environment <math>s</math> and produces a [[probability distribution]] <math>\pi_\theta(\cdot | s)</math>.

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The goal of policy gradient method is to optimize <math>J(\theta)</math> by [[Gradient descent|gradient ascent]] on the policy gradient <math>\nabla J(\theta)</math>.

As detailed on the [[Policy gradient method#Actor-critic methods|policy gradient method]] page, there are many [[Unbiasedunbiased estimator|unbiased estimators]]s of the policy gradient:<math display="block">\nabla_\theta J(\theta) = \mathbb{E}_{\pi_\theta}\left[\sum_{0\leq j \leq T} \nabla_\theta\ln\pi_\theta(A_j| S_j)

\cdot \Psi_j

\Big|S_0 = s_0 \right]</math>where <math display="inline">\Psi_j</math> is a linear sum of the following:

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* <math display="inline">\gamma^j \left(R_j + \gamma V^{\pi_\theta}( S_{j+1}) - V^{\pi_\theta}( S_{j})\right)</math>: [[Temporal difference learning|TD(1) learning]].

* <math display="inline">\gamma^j Q^{\pi_\theta}(S_j, A_j)</math>.

* <math display="inline">\gamma^j A^{\pi_\theta}(S_j, A_j)</math>: '''Advantage Actor-Critic (A2C)'''.<ref name=":0">{{Citation |lastlast1=Mnih |firstfirst1=Volodymyr |title=Asynchronous Methods for Deep Reinforcement Learning |date=2016-06-16 |url=https://arxiv.org/abs/1602.01783 |doi=10.48550/arXiv.1602.01783 |last2=Badia |first2=Adrià Puigdomènech |last3=Mirza |first3=Mehdi |last4=Graves |first4=Alex |last5=Lillicrap |first5=Timothy P. |last6=Harley |first6=Tim |last7=Silver |first7=David |last8=Kavukcuoglu |first8=Koray}}</ref>

* <math display="inline">\gamma^j \left(R_j + \gamma R_{j+1} + \gamma^2 V^{\pi_\theta}( S_{j+2}) - V^{\pi_\theta}( S_{j})\right)</math>: TD(2) learning.

* <math display="inline">\gamma^j \left(\sum_{k=0}^{n-1} \gamma^k R_{j+k} + \gamma^n V^{\pi_\theta}( S_{j+n}) - V^{\pi_\theta}( S_{j})\right)</math>: TD(n) learning.

* <math display="inline">\gamma^j \sum_{n=1}^\infty \frac{\lambda^{n-1}}{1-\lambda}\cdot \left(\sum_{k=0}^{n-1} \gamma^k R_{j+k} + \gamma^n V^{\pi_\theta}( S_{j+n}) - V^{\pi_\theta}( S_{j})\right)</math>: TD(λ) learning, also known as '''GAE (generalized advantage estimate)'''.<ref name="arxiv.org">{{Citation |lastlast1=Schulman |firstfirst1=John |title=High-Dimensional Continuous Control Using Generalized Advantage Estimation |date=2018-10-20 |url=https://arxiv.org/abs/1506.02438 |doi=10.48550/arXiv.1506.02438 |last2=Moritz |first2=Philipp |last3=Levine |first3=Sergey |last4=Jordan |first4=Michael |last5=Abbeel |first5=Pieter}}</ref> This is obtained by an exponentially decaying sum of the TD(n) learning terms.

=== Critic ===

In the unbiased estimators given above, certain functions such as <math>V^{\pi_\theta}, Q^{\pi_\theta}, A^{\pi_\theta}</math> appear. These are approximated by the '''critic'''. Since these functions all depend on the actor, the critic must learn alongside the actor. The critic is learned by value-based RL algorithms.

For example, if the critic is estimating the state-value function <math>V^{\pi_\theta}(s)</math>, then it can be learned by any value function approximation method. Let the critic be a function approximator <math>V_\phi(s)</math> with parameters <math>\phi</math>.

The simplest example is TD(1) learning, which trains the critic to minimize the TD(1) error:<math display="block">\delta_i = R_i + \gamma V_\phi(S_{i+1}) - V_\phi(S_i)</math>The critic parameters are updated by gradient descent on the squared TD error:<math display="block">\phi \leftarrow \phi - \alpha \nabla_\phi (\delta_i)^2 = \phi + \alpha \delta_i \nabla_\phi V_\phi(S_i)</math>where <math>\alpha</math> is the learning rate. Note that the gradient is taken with respect to the <math>\phi</math> in <math>V_\phi(S_i)</math> only, since the <math>\phi</math> in <math>\gamma V_\phi(S_{i+1})</math> constitutes a moving target, and the gradient is not taken with respect to that. This is a common source of error in implementations that use [[automatic differentiation]], and requires "stopping the gradient" at that point.

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</math>, low variance, high bias). This hyperparameter can be adjusted to pick the optimal bias-variance trade-off in advantage estimation. It uses an exponentially decaying average of n-step returns with <math>

\lambda

</math> being the decay strength.<ref name="arxiv.org"/>

</math> being the decay strength.<ref>{{Citation |last=Schulman |first=John |title=High-Dimensional Continuous Control Using Generalized Advantage Estimation |date=2018-10-20 |url=https://arxiv.org/abs/1506.02438 |doi=10.48550/arXiv.1506.02438 |last2=Moritz |first2=Philipp |last3=Levine |first3=Sergey |last4=Jordan |first4=Michael |last5=Abbeel |first5=Pieter}}</ref>

== Variants ==

* '''Asynchronous Advantage Actor-Critic (A3C)''': [[Parallel computing|Parallel and asynchronous]] version of A2C.<ref name=":0" />

* '''Soft Actor-Critic (SAC)''': Incorporates entropy maximization for improved exploration.<ref>{{Citation |lastlast1=Haarnoja |firstfirst1=Tuomas |title=Soft Actor-Critic Algorithms and Applications |date=2019-01-29 |url=https://arxiv.org/abs/1812.05905 |doi=10.48550/arXiv.1812.05905 |last2=Zhou |first2=Aurick |last3=Hartikainen |first3=Kristian |last4=Tucker |first4=George |last5=Ha |first5=Sehoon |last6=Tan |first6=Jie |last7=Kumar |first7=Vikash |last8=Zhu |first8=Henry |last9=Gupta |first9=Abhishek}}</ref>

* '''Deep Deterministic Policy Gradient (DDPG)''': Specialized for continuous action spaces.<ref>{{Citation |lastlast1=Lillicrap |firstfirst1=Timothy P. |title=Continuous control with deep reinforcement learning |date=2019-07-05 |url=https://arxiv.org/abs/1509.02971 |doi=10.48550/arXiv.1509.02971 |last2=Hunt |first2=Jonathan J. |last3=Pritzel |first3=Alexander |last4=Heess |first4=Nicolas |last5=Erez |first5=Tom |last6=Tassa |first6=Yuval |last7=Silver |first7=David |last8=Wierstra |first8=Daan}}</ref>

== See also ==

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== References ==

{{Reflist|30em}}

* {{Cite journal |lastlast1=Konda |firstfirst1=Vijay R. |last2=Tsitsiklis |first2=John N. |date=January 2003 |title=On Actor-Critic Algorithms |url=http://epubs.siam.org/doi/10.1137/S0363012901385691 |journal=SIAM Journal on Control and Optimization |language=en |volume=42 |issue=4 |pages=1143–1166 |doi=10.1137/S0363012901385691 |issn=0363-0129|url-access=subscription }}

* {{Cite book |lastlast1=Sutton |firstfirst1=Richard S. |title=Reinforcement learning: an introduction |last2=Barto |first2=Andrew G. |date=2018 |publisher=The MIT Press |isbn=978-0-262-03924-6 |edition=2 |series=Adaptive computation and machine learning series |___location=Cambridge, Massachusetts}}

* {{Cite book |last=Bertsekas |first=Dimitri P. |title=Reinforcement learning and optimal control |date=2019 |publisher=Athena Scientific |isbn=978-1-886529-39-7 |edition=2 |___location=Belmont, Massachusetts}}

* {{Cite book |last=Grossi |first=Csaba |title=Algorithms for Reinforcement Learning |date=2010 |publisher=Springer International Publishing |isbn=978-3-031-00423-0 |edition=1 |series=Synthesis Lectures on Artificial Intelligence and Machine Learning |___location=Cham}}

* {{Cite journal |last1=Grondman |first1=Ivo |last2=Busoniu |first2=Lucian |last3=Lopes |first3=Gabriel A. D. |last4=Babuska |first4=Robert |date=November 2012 |title=A Survey of Actor-Critic Reinforcement Learning: Standard and Natural Policy Gradients |journal=IEEE Transactions on Systems, Man, and Cybernetics - Part C: Applications and Reviews |volume=42 |issue=6 |pages=1291–1307 |doi=10.1109/TSMCC.2012.2218595 |bibcode=2012ITHMS..42.1291G |issn=1094-6977 |url=https://hal.science/hal-00756747 }}

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