Analyzing Equilibrium Bias in Risk-Sensitive Multi-Agent Reinforcement Learning

Kernkonzepte

The core message of this paper is that a naive definition of regret in risk-sensitive multi-agent reinforcement learning can lead to equilibrium bias, where the most risk-sensitive agents are favored at the expense of the other agents. The authors propose a new notion of risk-balanced regret to address this issue.

Zusammenfassung

The paper studies the problem of risk-sensitive multi-agent reinforcement learning (MARL) in general-sum Markov games, where agents optimize the entropic risk measure of rewards with potentially diverse risk preferences.
The key insights are:

Using the regret metric naively adapted from the risk-neutral setting can induce policies with equilibrium bias that favor the most risk-sensitive agents and overlook the other agents. This is demonstrated through a lower bound.

To address the issue of equilibrium bias, the authors propose a novel notion of regret, called risk-balanced regret, which accounts for the risk sensitivity of each agent and treats all agents symmetrically.

The authors develop a self-play algorithm for learning Nash, correlated, and coarse correlated equilibria in risk-sensitive Markov games. They prove that the proposed algorithm attains near-optimal regret guarantees with respect to the risk-balanced regret.

The paper provides the first finite-sample guarantees in risk-sensitive MARL based on the entropic risk measure.

Statistiken

The following sentences contain key metrics or figures:
The regret is defined as the sum of the regrets on the worst performing agent at each episode.
The risk-balanced regret takes into account the risk sensitivity of each agent and treats all agents symmetrically.
The authors prove a lower bound on the risk-balanced regret, which suggests that it addresses the problem of equilibrium bias suffered by the naive regret.
The authors prove that their proposed algorithm achieves a nearly optimal upper bound for the risk-balanced regret.

Zitate

"We show that using the regret naively adapted from existing literature as a performance metric could induce policies with equilibrium bias that favor the most risk-sensitive agents and overlook the other agents."
"To address such deficiency of the naive regret, we propose a novel notion of regret, which we call risk-balanced regret, and show through a lower bound that it overcomes the issue of equilibrium bias."
"Furthermore, we develop a self-play algorithm for learning Nash, correlated, and coarse correlated equilibria in risk-sensitive Markov games. We prove that the proposed algorithm attains near-optimal regret guarantees with respect to the risk-balanced regret."

Wichtige Erkenntnisse aus

Taming Equilibrium Bias in Risk-Sensitive Multi-Agent Reinforcement Learning

by Yingjie Fei,... um arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.02724.pdf

Tiefere Fragen

How can the proposed risk-balanced regret be extended to other risk measures beyond the entropic risk

The proposed risk-balanced regret can be extended to other risk measures beyond the entropic risk by modifying the formulation to accommodate different risk preferences and measures. For example, instead of using the entropic risk measure in the regret calculation, one could incorporate other risk measures such as variance, conditional value at risk (CVaR), or expected shortfall. By adjusting the regret calculation to consider these alternative risk measures, the risk-balanced regret can be tailored to reflect a broader range of risk preferences and sensitivities among the agents in the multi-agent system.

What are the practical implications of equilibrium bias in real-world applications of risk-sensitive multi-agent systems, and how can the risk-balanced regret approach help mitigate these issues

Equilibrium bias in real-world applications of risk-sensitive multi-agent systems can have significant practical implications, leading to unfair advantages for certain agents based on their risk preferences. In investment scenarios, this bias could result in disproportionate benefits for risk-seeking investors while disadvantaging risk-averse investors. Similarly, in gaming environments, equilibrium bias could create imbalances favoring aggressive players over cautious ones, impacting the overall gaming experience.
The risk-balanced regret approach can help mitigate these issues by providing a more equitable and balanced evaluation of algorithm performance in risk-sensitive multi-agent systems. By considering the risk preferences of all agents and ensuring that the regret calculation accounts for the diverse risk sensitivities present, the risk-balanced regret approach helps prevent algorithms from favoring one type of agent over others. This can lead to fairer outcomes and more inclusive decision-making processes in multi-agent systems.

What are the connections between the risk-balanced regret and other notions of fairness or equity in multi-agent systems

The risk-balanced regret concept has connections to other notions of fairness or equity in multi-agent systems, particularly in terms of ensuring equal treatment and consideration for agents with varying risk preferences. By incorporating the risk-balanced regret into the evaluation of algorithm performance, the approach promotes a more balanced and unbiased assessment of outcomes for all agents involved. This aligns with principles of fairness and equity by preventing algorithms from disproportionately favoring or disadvantaging certain agents based on their risk sensitivities.
Furthermore, the risk-balanced regret approach can contribute to promoting diversity and inclusivity in multi-agent systems by acknowledging and accommodating the different risk preferences of agents. By providing a framework that accounts for heterogeneous risk profiles and ensures that all agents are treated fairly in the decision-making process, the risk-balanced regret approach supports a more equitable and harmonious environment for collaboration and interaction among agents.