Bayesian policy gradient and actor-critic algorithms
Authors: Mohammad Ghavamzadeh, Yaakov Engel, Michal Valko
Organizations: Adobe Research & Inria · Rafael Advanced Defence System, Israel · Inria Lille — SequeL team, France
Abstract
Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policy by following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate the gradient, which tend to have high variance, requiring many samples and resulting in slow convergence. We first propose a Bayesian framework for policy gradient, based on modeling the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient and a measure of the uncertainty in the gradient estimates, namely, the gradient covariance, are provided at little extra cost. Since the proposed framework considers system trajectories as its basic observable unit, it does not require the dynamics within trajectories to be of any particular form, and can be extended to partially observable problems. On the downside, it cannot exploit the Markov property when the system is Markovian. To address this, we supplement our Bayesian policy gradient framework with a new actor-critic learning model in which a Bayesian class of non-parametric critics, based on Gaussian process temporal difference learning, is used. Such critics model the action-value function as a Gaussian process, allowing Bayes rule to be used to compute the posterior distribution over action-value functions, conditioned on the observed data. Appropriate choices of the policy parameterization and of the prior covariance (kernel) between action-values yield closed-form expressions for the posterior of the gradient of the expected return with respect to the policy parameters. We perform detailed experimental comparisons of the proposed Bayesian policy gradient and actor-critic algorithms with classic Monte-Carlo based policy gradient methods, on a number of reinforcement learning problems.
Reinforcement Learning (RL) is a sequential decision-making framework in which an agent learns optimal policies through interaction with an environment by maximizing cumulative rewards. Among RL methods, Bayesian Reinforcement Learning (BRL) addresses common practical challenges related to data scarcity by leveraging prior knowledge about the environment and sequential belief updates. However, most BRL approaches require an explicit likelihood function, which is frequently inaccessible or intractable in real-world settings. We propose Likelihood-Free Iterated Batch Importance Sampling (LF-IBIS), a novel algorithm for BRL that updates the agent's beliefs online as new interactions become available. By combining Approximate Bayesian Computation with Iterated Batch Importance Sampling, LF-IBIS enables full Bayesian inference in settings where the environment dynamics are not described by an explicit or tractable likelihood. The method yields approximate posterior distributions over both environment parameters and optimal policies, providing a quantification of policy uncertainty useful for a Bayesian treatment of the exploration-exploitation trade-off. We test the method on a simulation study in response-adaptive randomization in clinical trials, where closed-form posteriors enable validation. Additional experiments address settings where the posterior has no closed form and illustrate online policy updating based on the posterior distribution of the optimal policy.
The framework of robust Markov decision processes (RMDPs) allows the design of reinforcement learning agents that satisfy performance guarantees under worst-case transition dynamics. Traditional RMDPs consider discrete-time dynamics and recently, sample-efficient policy gradient algorithms have been considered in this context. This paper investigates policy gradient algorithms within a continuous-time RMDP framework. Policy gradients and adversarial gradients are derived using pathwise and adjoint-based formulas for stochastic and ordinary differential equations. We propose double-loop optimisers to obtain linear convergence in the oracle-based setting and an O~(ε21) sample complexity in the sample-based setting in an analysis which also derives novel tools for the framework of undiscounted total cost MDPs. Additionally, we propose mean-field optimisers as distributional optimisers with an O~(K1) oracle-based convergence rate and an O~(εN2) sample complexity under N-particle approximation. The effectiveness of continuous-time policy gradient algorithms is confirmed for both optimisers on continuous-time RMDPs with neural ordinary differential equation dynamics.
Tanya Veeravalli, David M. Bossens, Atsushi Nitanda
Mixture policies theoretically offer greater flexibility than unimodal policies in continuous action reinforcement learning, but the practical benefits of this complexity remain elusive. Mixture policies are notably absent from most state-of-the-art algorithms, raising a fundamental question: Is the added representational overhead useful? We show that increased flexibility can theoretically enhance solution quality and entropy robustness. Yet standard algorithms like SAC do not leverage these advantages. A core issue is the lack of a low-variance reparameterization trick for mixtures, a luxury Gaussian policies enjoy. We propose a marginalized reparameterization (MRP) estimator to address this, proving it offers lower variance than the standard likelihood-ratio (LR) approach. Our experiments across Gym MuJoCo, DeepMind Control Suite, and MetaWorld show that MRP mixture policies significantly outperform their LR ones, and reach parity (sometimes better) with Gaussian counterparts. In addition, we do find several cases where MRP mixture policies exhibit clear empirical advantages. In this paper, we provide a clearer understanding of the trade-offs involved, elevating MRP mixture policies from theoretical curiosity to a practical tool.