Matthew Fellows

Matthew Fellows, Kristian Hartikainen, Shimon Whiteson

We introduce a novel perspective on Bayesian reinforcement learning (RL); whereas existing approaches infer a posterior over the transition distribution or Q-function, we characterise the uncertainty in the Bellman operator. Our Bayesian Bellman operator (BBO) framework is motivated by the insight that when bootstrapping is introduced, model-free approaches actually infer a posterior over Bellman operators, not value functions. In this paper, we use BBO to provide a rigorous theoretical analysis of model-free Bayesian RL to better understand its relationshipto established frequentist RL methodologies. We prove that Bayesian solutions are consistent with frequentist RL solutions, even when approximate inference isused, and derive conditions for which convergence properties hold. Empirically, we demonstrate that algorithms derived from the BBO framework have sophisticated deep exploration properties that enable them to solve continuous control tasks at which state-of-the-art regularised actor-critic algorithms fail catastrophically

Matthew Fellows, Anuj Mahajan, Tim G. J. Rudner et al.

Applying probabilistic models to reinforcement learning (RL) enables the application of powerful optimisation tools such as variational inference to RL. However, existing inference frameworks and their algorithms pose significant challenges for learning optimal policies, e.g., the absence of mode capturing behaviour in pseudo-likelihood methods and difficulties learning deterministic policies in maximum entropy RL based approaches. We propose VIREL, a novel, theoretically grounded probabilistic inference framework for RL that utilises a parametrised action-value function to summarise future dynamics of the underlying MDP. This gives VIREL a mode-seeking form of KL divergence, the ability to learn deterministic optimal polices naturally from inference and the ability to optimise value functions and policies in separate, iterative steps. In applying variational expectation-maximisation to VIREL we thus show that the actor-critic algorithm can be reduced to expectation-maximisation, with policy improvement equivalent to an E-step and policy evaluation to an M-step. We then derive a family of actor-critic methods from VIREL, including a scheme for adaptive exploration. Finally, we demonstrate that actor-critic algorithms from this family outperform state-of-the-art methods based on soft value functions in several domains.

Matthew Fellows, Kamil Ciosek, Shimon Whiteson

We propose a new way of deriving policy gradient updates for reinforcement learning. Our technique, based on Fourier analysis, recasts integrals that arise with expected policy gradients as convolutions and turns them into multiplications. The obtained analytical solutions allow us to capture the low variance benefits of EPG in a broad range of settings. For the critic, we treat trigonometric and radial basis functions, two function families with the universal approximation property. The choice of policy can be almost arbitrary, including mixtures or hybrid continuous-discrete probability distributions. Moreover, we derive a general family of sample-based estimators for stochastic policy gradients, which unifies existing results on sample-based approximation. We believe that this technique has the potential to shape the next generation of policy gradient approaches, powered by analytical results.