Scalable Submodular Policy Optimization via Pruned Submodularity Graph

TL;DR

This paper introduces a scalable method for optimizing policies in reinforcement learning with submodular reward functions, achieving better rewards efficiently compared to baseline methods.

Contribution

It proposes a pruned submodularity graph-based approach for approximate policy optimization in submodular RL problems, with theoretical guarantees and empirical validation.

Findings

The method outperforms baseline algorithms in reward maximization.

It offers a provable approximation with feasible computational complexity.

Experimental results demonstrate improved policy performance.

Abstract

In Reinforcement Learning (abbreviated as RL), an agent interacts with the environment via a set of possible actions, and a reward is generated from some unknown distribution. The task here is to find an optimal set of actions such that the reward after a certain time step gets maximized. In a traditional setup, the reward function in an RL Problem is considered additive. However, in reality, there exist many problems, including path planning, coverage control, etc., the reward function follows the diminishing return, which can be modeled as a submodular function. In this paper, we study a variant of the RL Problem where the reward function is submodular, and our objective is to find an optimal policy such that this reward function gets maximized. We have proposed a pruned submodularity graph-based approach that provides a provably approximate solution in a feasible computation time. The proposed approach has been analyzed to understand its time and space requirements as well as a performance guarantee. We have experimented with a benchmark agent-environment setup, which has been used for similar previous studies, and the results are reported. From the results, we observe that the policy obtained by our proposed approach leads to more reward than the baseline methods.