# PRISM: Parallel Reward Integration with Symmetry for MORL

arXiv: https://arxiv.org/abs/2602.18277 · HTML: https://mlsanity.com/paper/2602.18277/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 20 Feb 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 28 of 28)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progress](https://mlsanity.com/paper/1806.06877/) (2018)
- [A Practical Guide to Multi-Objective Reinforcement Learning and Planning](https://mlsanity.com/paper/2103.09568/) (2021)
- [A Generalized Algorithm for Multi-Objective Reinforcement Learning and Policy Adaptation](https://mlsanity.com/paper/1908.08342/) (2019)
- [Deep Reinforcement Learning for Robotics: A Survey of Real-World Successes](https://mlsanity.com/paper/2408.03539/) (2024)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [A survey on intrinsic motivation in reinforcement learning](https://mlsanity.com/paper/1908.06976/) (2019)
- [Equivariant Q Learning in Spatial Action Spaces](https://mlsanity.com/paper/2110.15443/) (2021)
- [Sample-Efficient Multi-Objective Learning via Generalized Policy Improvement Prioritization](https://mlsanity.com/paper/2301.07784/) (2023)
- [Why ResNet Works? Residuals Generalize](https://mlsanity.com/paper/1904.01367/) (2019)
- [Self-Supervised Online Reward Shaping in Sparse-Reward Environments](https://mlsanity.com/paper/2103.04529/) (2021)
- [Meta-Learning for Multi-objective Reinforcement Learning](https://mlsanity.com/paper/1811.03376/) (2018)
- [Learning Long-Term Reward Redistribution via Randomized Return Decomposition](https://mlsanity.com/paper/2111.13485/) (2021)
- [Learning Guidance Rewards with Trajectory-space Smoothing](https://mlsanity.com/paper/2010.12718/) (2020)
- [On the Generalization Gap in Reparameterizable Reinforcement Learning](https://mlsanity.com/paper/1905.12654/) (2019)
- [Pareto Set Learning for Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2501.06773/) (2025)
- [Approximate Equivariance in Reinforcement Learning](https://mlsanity.com/paper/2411.04225/) (2024)
- [Benefits of Permutation-Equivariance in Auction Mechanisms](https://mlsanity.com/paper/2210.05579/) (2022)
- [Preference-based Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2507.14066/) (2025)
- [Attention-Based Reward Shaping for Sparse and Delayed Rewards](https://mlsanity.com/paper/2505.10802/) (2025)
- [Beyond Simple Sum of Delayed Rewards: Non-Markovian Reward Modeling for Reinforcement Learning](https://mlsanity.com/paper/2410.20176/) (2024)
- [Multi-Objective Reinforcement Learning for Power Grid Topology Control](https://mlsanity.com/paper/2502.00040/) (2025)

## Built on by (most cited first, 1 of 1)

- [GameSmith: Scaling Zero-Sum Self-Play with Synthesised Games](https://mlsanity.com/paper/2610.13995/) (2026)

## Abstract (arXiv)

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 hrefhttps://github.com/EVIEHub/PRISMhttps://github.com/EVIEHub/PRISM.