PRISM: Parallel Reward Integration with Symmetry for MORL

TL;DR

PRISM introduces a symmetry-based approach to improve sample efficiency and performance in heterogeneous Multi-Objective Reinforcement Learning by aligning reward channels and constraining policy search.

Contribution

It proposes ReSymNet and SymReg to address temporal-frequency mismatches and enforce reflectional symmetry, enhancing learning and generalization in MORL.

Findings

Outperforms baseline and oracle methods in MuJoCo benchmarks

Achieves over 100% hypervolume gains compared to sparse-reward baseline

Improves Pareto coverage and distributional balance

Abstract

This work studies heterogeneous Multi-Objective Reinforcement Learning (MORL), where objectives can differ sharply in temporal frequency. Such heterogeneity allows dense objectives to dominate learning, while sparse long-horizon rewards receive weak credit assignment, leading to poor sample efficiency. We propose a Parallel Reward Integration with Symmetry (PRISM) algorithm that enforces reflectional symmetry as an inductive bias in aligning reward channels. PRISM introduces ReSymNet, a theory-motivated model that reconciles temporal-frequency mismatches across objectives, using residual blocks to learn a scaled opportunity value that accelerates exploration while preserving the optimal policy. We also propose SymReg, a reflectional equivariance regulariser that enforces agent mirroring and constrains policy search to a reflection-equivariant subspace. This restriction provably reduces hypothesis complexity and improves generalisation. Across MuJoCo benchmarks, PRISM consistently outperforms both a sparse-reward baseline and an oracle trained with full dense rewards, improving Pareto coverage and distributional balance: it achieves hypervolume gains exceeding 100\% over the baseline and up to 32\% over the oracle. The code is at \href{https://github.com/EVIEHub/PRISM}{https://github.com/EVIEHub/PRISM}.