Rahul V. Kulkarni

Jacob Adamczyk, Argenis Arriojas, Stas Tiomkin et al.

In reinforcement learning (RL), the ability to utilize prior knowledge from previously solved tasks can allow agents to quickly solve new problems. In some cases, these new problems may be approximately solved by composing the solutions of previously solved primitive tasks (task composition). Otherwise, prior knowledge can be used to adjust the reward function for a new problem, in a way that leaves the optimal policy unchanged but enables quicker learning (reward shaping). In this work, we develop a general framework for reward shaping and task composition in entropy-regularized RL. To do so, we derive an exact relation connecting the optimal soft value functions for two entropy-regularized RL problems with different reward functions and dynamics. We show how the derived relation leads to a general result for reward shaping in entropy-regularized RL. We then generalize this approach to derive an exact relation connecting optimal value functions for the composition of multiple tasks in entropy-regularized RL. We validate these theoretical contributions with experiments showing that reward shaping and task composition lead to faster learning in various settings.

Argenis Arriojas, Jacob Adamczyk, Stas Tiomkin et al.

Reinforcement learning (RL) is an important field of research in machine learning that is increasingly being applied to complex optimization problems in physics. In parallel, concepts from physics have contributed to important advances in RL with developments such as entropy-regularized RL. While these developments have led to advances in both fields, obtaining analytical solutions for optimization in entropy-regularized RL is currently an open problem. In this paper, we establish a mapping between entropy-regularized RL and research in non-equilibrium statistical mechanics focusing on Markovian processes conditioned on rare events. In the long-time limit, we apply approaches from large deviation theory to derive exact analytical results for the optimal policy and optimal dynamics in Markov Decision Process (MDP) models of reinforcement learning. The results obtained lead to a novel analytical and computational framework for entropy-regularized RL which is validated by simulations. The mapping established in this work connects current research in reinforcement learning and non-equilibrium statistical mechanics, thereby opening new avenues for the application of analytical and computational approaches from one field to cutting-edge problems in the other.