Non-Ergodic Reinforcement Learning: Transforming Returns for Robust Policies

Core Concepts

Optimizing the expected value of non-ergodic rewards can lead to policies that receive exceptionally high returns with probability zero but almost surely result in catastrophic outcomes. Transforming the returns to have ergodic increments enables learning robust policies by optimizing the long-term return for individual agents rather than the average across infinitely many trajectories.

Abstract

The paper discusses the impact of ergodicity on the choice of the optimization criterion in reinforcement learning (RL). If the rewards are non-ergodic, focusing on the expected return yields non-robust policies that are commonly found with conventional RL algorithms. The key insights are: Non-ergodicity: In non-ergodic settings, the average over many trajectories (expected value) differs from the average along one long trajectory. This can lead to policies that perform exceptionally well on average but fail catastrophically in individual instances. Ergodicity transformation: An alternative to changing the objective function is to find a transformation that converts the time series of returns into one with ergodic increments. Optimizing the expected value of these ergodic increments is equivalent to maximizing the long-term growth rate of the return for individual agents. Learning the transformation: The paper proposes a method for learning an ergodicity transformation directly from data, without requiring analytical expressions for the environment dynamics. Relation to risk-sensitive RL: The authors analyze how transformations used in risk-sensitive RL can be motivated from an ergodicity perspective, providing a theoretical foundation for these approaches. Experiments: The authors demonstrate the effectiveness of the proposed transformation on standard RL benchmark environments, showing that it can lead to more robust policies compared to standard RL algorithms. The paper highlights the importance of considering ergodicity when designing RL algorithms, especially in domains where the consequences of failure can be catastrophic. The proposed approach provides a principled way to learn policies that optimize the long-term performance of individual agents rather than the average across many trajectories.

Stats

The paper does not contain any key metrics or important figures to support the author's key logics. The analysis is primarily conceptual, focusing on the theoretical implications of non-ergodicity in reinforcement learning.

Quotes

The paper does not contain any striking quotes supporting the author's key logics.

Key Insights Distilled From

Non-ergodicity in reinforcement learning

by Domi... at arxiv.org 04-12-2024

https://arxiv.org/pdf/2310.11335.pdf

Deeper Inquiries

What are the implications of non-ergodicity for multi-agent reinforcement learning, where the actions of one agent can affect the rewards of others

In multi-agent reinforcement learning, non-ergodicity can have significant implications due to the interconnected nature of the agents' actions and rewards. When one agent's actions impact the rewards of others, non-ergodicity can lead to challenges in optimizing policies that benefit the entire group. For example, in a scenario where agents are collaborating to achieve a common goal, non-ergodic rewards can result in suboptimal decision-making. If the rewards are non-ergodic, the expected value of the return may not accurately reflect the long-term performance of the agents. This can lead to policies that prioritize short-term gains or risky strategies that benefit individual agents but harm the collective outcome. To address this issue, incorporating ergodicity transformations in multi-agent reinforcement learning can help optimize policies that consider the long-term growth rate of the return for the entire group. By transforming the rewards to have ergodic increments, agents can learn robust policies that account for the interconnected dynamics of the system and promote cooperative behavior among the agents.

How can the ergodicity transformation be extended to handle state-dependent returns, where the transformation may need to depend on the current state of the system

Extending the ergodicity transformation to handle state-dependent returns involves adapting the transformation to consider the current state of the system when converting the returns into a time series with ergodic increments. In this context, the transformation would need to be tailored to the specific state-space of the environment, ensuring that the increments remain ergodic regardless of the state transitions. One approach to incorporating state-dependent transformations is to introduce a mapping function that takes into account the current state of the system when applying the transformation to the returns. This mapping function can adjust the transformation parameters based on the state variables, allowing for a more dynamic and adaptive transformation process. By incorporating state-dependent transformations, agents can learn policies that are optimized for the long-term growth rate of the return while considering the unique characteristics of the environment at each state transition. This approach enhances the adaptability and robustness of the reinforcement learning algorithms in handling complex and dynamic state spaces.

Can the insights from this paper be used to develop new reinforcement learning algorithms that directly optimize for the long-term growth rate of the return, without the need for a separate transformation step

The insights from this paper can indeed be leveraged to develop new reinforcement learning algorithms that directly optimize for the long-term growth rate of the return without the need for a separate transformation step. By integrating the concept of ergodicity directly into the algorithm design, researchers can create novel RL approaches that prioritize the individual agent's long-term performance over the expected value of the return. One potential approach is to design algorithms that inherently consider the ergodic properties of the rewards and optimize policies based on the time-average growth rate of the return. By incorporating ergodicity principles into the algorithm's objective function and learning process, agents can learn robust and sustainable policies that account for the non-ergodic nature of the rewards. Furthermore, developing algorithms that directly optimize for the long-term growth rate of the return can lead to more efficient and effective decision-making in complex environments where non-ergodicity poses challenges. By focusing on the individual agent's performance over time, these algorithms can promote stable and reliable behavior that benefits the agents and the overall system.