Dual-Objective Reinforcement Learning with Novel Hamilton-Jacobi-Bellman Formulations

• URL: http://arxiv.org/abs/2506.16016v1
• Date: Thu, 19 Jun 2025 04:27:17 GMT
• Title: Dual-Objective Reinforcement Learning with Novel Hamilton-Jacobi-Bellman Formulations
• Authors: William Sharpless, Dylan Hirsch, Sander Tonkens, Nikhil Shinde, Sylvia Herbert,
• Abstract summary: Hard constraints in reinforcement learning (RL) often degrade policy performance.<n>We extend recent advances that connect Hamilton-Jacobi equations with RL to propose two novel value functions for dual-objective satisfaction.<n>We propose a variation of Proximal Policy Optimization (DO-HJ-PPO) which solves these problems.
• Score: 0.5937476291232802
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Hard constraints in reinforcement learning (RL), whether imposed via the reward function or the model architecture, often degrade policy performance. Lagrangian methods offer a way to blend objectives with constraints, but often require intricate reward engineering and parameter tuning. In this work, we extend recent advances that connect Hamilton-Jacobi (HJ) equations with RL to propose two novel value functions for dual-objective satisfaction. Namely, we address: (1) the Reach-Always-Avoid problem - of achieving distinct reward and penalty thresholds - and (2) the Reach-Reach problem - of achieving thresholds of two distinct rewards. In contrast with temporal logic approaches, which typically involve representing an automaton, we derive explicit, tractable Bellman forms in this context by decomposing our problem into reach, avoid, and reach-avoid problems, as to leverage these aforementioned recent advances. From a mathematical perspective, the Reach-Always-Avoid and Reach-Reach problems are complementary and fundamentally different from standard sum-of-rewards problems and temporal logic problems, providing a new perspective on constrained decision-making. We leverage our analysis to propose a variation of Proximal Policy Optimization (DO-HJ-PPO), which solves these problems. Across a range of tasks for safe-arrival and multi-target achievement, we demonstrate that DO-HJ-PPO produces qualitatively distinct behaviors from previous approaches and out-competes a number of baselines in various metrics.

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