# Bounding the Optimal Value Function in Compositional Reinforcement Learning

arXiv: https://arxiv.org/abs/2303.02557 · HTML: https://mlsanity.com/paper/2303.02557/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 5 Mar 2023.

## Builds on (most cited first, 13 of 13)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Successor Features for Transfer in Reinforcement Learning](https://mlsanity.com/paper/1606.05312/) (2016)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [SUNRISE: A Simple Unified Framework for Ensemble Learning in Deep Reinforcement Learning](https://mlsanity.com/paper/2007.04938/) (2020)
- [MCP: Learning Composable Hierarchical Control with Multiplicative Compositional Policies](https://mlsanity.com/paper/1905.09808/) (2019)
- [Composable Deep Reinforcement Learning for Robotic Manipulation](https://mlsanity.com/paper/1803.06773/) (2018)
- [The Option Keyboard: Combining Skills in Reinforcement Learning](https://mlsanity.com/paper/2106.13105/) (2021)
- [A Boolean Task Algebra for Reinforcement Learning](https://mlsanity.com/paper/2001.01394/) (2020)
- [Constructing a Good Behavior Basis for Transfer using Generalized Policy Updates](https://mlsanity.com/paper/2112.15025/) (2021)
- [Bilinear value networks](https://mlsanity.com/paper/2204.13695/) (2022)
- [Utilizing Prior Solutions for Reward Shaping and Composition in Entropy-Regularized Reinforcement Learning](https://mlsanity.com/paper/2212.01174/) (2022)

## Built on by (most cited first, 3 of 3)

- [Boosting Soft Q-Learning by Bounding](https://mlsanity.com/paper/2406.18033/) (2024)
- [Is Temporal Difference Learning the Gold Standard for Stitching in RL?](https://mlsanity.com/paper/2510.21995/) (2025)
- [Goals and the Structure of Experience](https://mlsanity.com/paper/2508.15013/) (2025)

## Abstract (arXiv)

In the field of reinforcement learning (RL), agents are often tasked with solving a variety of problems differing only in their reward functions. In order to quickly obtain solutions to unseen problems with new reward functions, a popular approach involves functional composition of previously solved tasks. However, previous work using such functional composition has primarily focused on specific instances of composition functions whose limiting assumptions allow for exact zero-shot composition. Our work unifies these examples and provides a more general framework for compositionality in both standard and entropy-regularized RL. We find that, for a broad class of functions, the optimal solution for the composite task of interest can be related to the known primitive task solutions. Specifically, we present double-sided inequalities relating the optimal composite value function to the value functions for the primitive tasks. We also show that the regret of using a zero-shot policy can be bounded for this class of functions. The derived bounds can be used to develop clipping approaches for reducing uncertainty during training, allowing agents to quickly adapt to new tasks.