Policy Gradient for Reinforcement Learning with General Utilities

TL;DR

This paper extends reinforcement learning to optimize general, possibly non-linear utilities of policies, deriving a policy gradient theorem that broadens the scope of RL applications beyond linear reward functions.

Contribution

The authors derive a novel policy gradient theorem for RL with general utilities, enabling optimization of non-linear objectives in reinforcement learning.

Findings

Derived a policy gradient theorem for non-linear utilities

Presented a simple sample-based algorithm based on the theorem

Broadens RL applicability to complex, non-linear objectives

Abstract

In Reinforcement Learning (RL), the goal of agents is to discover an optimal policy that maximizes the expected cumulative rewards. This objective may also be viewed as finding a policy that optimizes a linear function of its state-action occupancy measure, hereafter referred as Linear RL. However, many supervised and unsupervised RL problems are not covered in the Linear RL framework, such as apprenticeship learning, pure exploration and variational intrinsic control, where the objectives are non-linear functions of the occupancy measures. RL with non-linear utilities looks unwieldy, as methods like Bellman equation, value iteration, policy gradient, dynamic programming that had tremendous success in Linear RL, fail to trivially generalize. In this paper, we derive the policy gradient theorem for RL with general utilities. The policy gradient theorem proves to be a cornerstone in Linear RL due to its elegance and ease of implementability. Our policy gradient theorem for RL with general utilities shares the same elegance and ease of implementability. Based on the policy gradient theorem derived, we also present a simple sample-based algorithm. We believe our results will be of interest to the community and offer inspiration to future works in this generalized setting.