Anderson Acceleration for Reinforcement Learning
This paper discusses a method called Anderson acceleration, which can make reinforcement learning algorithms faster by improving how they compute optimal decisions.
This video presentation explains the key concepts from the paper in plain language.
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- 1 The new estimate is obtained by applying the operator to the vector u1e7du03b1 k+1 of minimal residual.
- 2 The estimate u03b1 k+1 is biased as being the solution to a residual problem with sampled transitions.
- 3 This gradient can be estimated with rollouts but it is quite common to estimate the Q-function itself.
- 4 It is quite common to estimate the critic using a SARSA-like approach especially in deep RL.
Introduction
Reinforcement learning (RL) is intrinsically linked to fixed-point computation because the optimal value function is the fixed point of the (nonlinear) Bellman optimality operator and the value function of a given policy is the fixed point of the related (linear) Bellman evaluation operator. These fixed points are most often computed recursively by repeatedly applying the operator of interest.
The evaluation step of policy iteration and the least-squares temporal differences (LSTD) algorithm are notable exceptions to recursive fixed-point computation.
Anderson acceleration searches for the point with minimal residual within the subspace spanned by the previous estimates and applies the operator to it.
Methodology
Anderson acceleration is a method that speeds up the computation of fixed points. Anderson acceleration would modify the targets in the regression problem with coefficients obtained with a cheap least-squares.
Study Design
Results & Findings
The classic fixed-point iteration repeatedly applies the operator to the last estimate. The new estimate is given by the following formula.
- The classic fixed-point iteration repeatedly applies the operator to the last estimate.
- The new estimate is given by the following formula.
- The new estimate is obtained by applying the operator to the vector u1e7du03b1 k+1 of minimal residual.
- We run all algorithms for 250 iterations and measure the normalised error for algorithm alg.
- Anderson acceleration consistently offers a significant speed-up compared to value iteration and small values of m around 5 seem to be enough.
The new estimate is obtained by applying the operator to the vector u1e7du03b1 k+1 of minimal residual.
The estimate u03b1 k+1 is biased as being the solution to a residual problem with sampled transitions.
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Practical Applications
We consider the u2113 2 -norm for this problem but it could be a different norm such as u2113 1 or u2113 u221e. It could still be interesting for policy evaluation or in the approximate setting.
We discuss briefly its possible applications to (deep) RL.
Anderson acceleration could be applied to approximate dynamic programming and related methods.
Anderson Acceleration for Value Iteration
This section reviews Markov decision processes and value iteration, demonstrating how Anderson acceleration can enhance convergence speed in these contexts.
Value Iteration
Value iteration is defined within the framework of Markov Decision Processes (MDPs), detailing the components such as state space, action space, transition kernel, and reward function, culminating in the value iteration algorithm.
Accelerated Value Iteration
The section describes the implementation of Anderson acceleration in the context of the Bellman operator, providing a detailed algorithm for accelerated value iteration.
Figures Explained
Frequently Asked Questions
The evaluation step of policy iteration and the least-squares temporal differences (LSTD) algorithm are notable exceptions to recursive fixed-point computation. Anderson acceleration has been successfully applied to electronic structure computation and computational chemistry but has never been applied to dynamic programming or.
Anderson acceleration is a method that speeds up the computation of fixed points. Anderson acceleration would modify the targets in the regression problem with coefficients obtained with a cheap least-squares.
The new estimate is obtained by applying the operator to the vector u1e7du03b1 k+1 of minimal residual. The estimate u03b1 k+1 is biased as being the solution to a residual problem with sampled transitions.
We consider the u2113 2 -norm for this problem but it could be a different norm such as u2113 1 or u2113 u221e. It could still be interesting for policy evaluation or in the approximate setting.
This paper discusses a method called Anderson acceleration, which can make reinforcement learning algorithms faster by improving how they compute optimal decisions.
Yes. PDFDigest can turn this paper into a structured explanation, key takeaways, visual summaries, and a narrated video when available.