Multi-Agent Lipschitz Bandits
arXiv:2602.16965v1 Announce Type: new Abstract: We study the decentralized multi-player stochastic bandit problem over a continuous, Lipschitz-structured action space where hard collisions yield zero reward. Our objective is to design a communication-free policy that maximizes collective reward, with coordination costs that are independent of the time horizon $T$. We propose a modular protocol that first solves the multi-agent coordination problem -- identifying and seating players on distinct high-value regions via a novel maxima-directed search -- and then decouples the problem into $N$ independent single-player Lipschitz bandits. We establish a near-optimal regret bound of $\tilde{O}(T^{(d+1)/(d+2)})$ plus a $T$-independent coordination cost, matching the single-player rate. To our knowledge, this is the first framework providing such guarantees, and it extends to general distance-threshold collision models.
arXiv:2602.16965v1 Announce Type: new Abstract: We study the decentralized multi-player stochastic bandit problem over a continuous, Lipschitz-structured action space where hard collisions yield zero reward. Our objective is to design a communication-free policy that maximizes collective reward, with coordination costs that are independent of the time horizon $T$. We propose a modular protocol that first solves the multi-agent coordination problem -- identifying and seating players on distinct high-value regions via a novel maxima-directed search -- and then decouples the problem into $N$ independent single-player Lipschitz bandits. We establish a near-optimal regret bound of $\tilde{O}(T^{(d+1)/(d+2)})$ plus a $T$-independent coordination cost, matching the single-player rate. To our knowledge, this is the first framework providing such guarantees, and it extends to general distance-threshold collision models.
Executive Summary
This article presents a novel approach to solving the decentralized multi-player stochastic bandit problem in a continuous, Lipschitz-structured action space. The proposed protocol, Multi-Agent Lipschitz Bandits, achieves a near-optimal regret bound of $ ilde{O}(T^{(d+1)/(d+2)})$ plus a $T$-independent coordination cost. This framework is significant as it extends to general distance-threshold collision models and provides a communication-free policy that maximizes collective reward. The authors' modular protocol first solves the multi-agent coordination problem and then decouples the problem into $N$ independent single-player Lipschitz bandits. This approach has potential applications in multi-agent systems, where coordination and communication can be costly and limited.
Key Points
- ▸ The article proposes a novel approach to solving the decentralized multi-player stochastic bandit problem in a continuous, Lipschitz-structured action space.
- ▸ The proposed protocol, Multi-Agent Lipschitz Bandits, achieves a near-optimal regret bound of $ ilde{O}(T^{(d+1)/(d+2)})$ plus a $T$-independent coordination cost.
- ▸ The framework extends to general distance-threshold collision models and provides a communication-free policy that maximizes collective reward.
Merits
Strength
The proposed protocol achieves a near-optimal regret bound, which is a significant improvement over existing methods. Additionally, the framework's extension to general distance-threshold collision models expands its applicability to various multi-agent systems.
Extension of Existing Work
The article builds upon existing work in multi-agent bandits, providing a novel approach that decouples the problem into $N$ independent single-player Lipschitz bandits, which is a significant contribution to the field.
Demerits
Limitation
The proposed protocol assumes a Lipschitz-structured action space, which might not be applicable to all multi-agent systems. Additionally, the coordination cost is $T$-independent, but the overall regret bound still depends on the time horizon $T$. Further research is needed to generalize the framework to more complex action spaces and reduce its dependence on $T$.
Expert Commentary
The article presents a novel approach to solving the decentralized multi-player stochastic bandit problem in a continuous, Lipschitz-structured action space. The proposed protocol, Multi-Agent Lipschitz Bandits, achieves a near-optimal regret bound of $ ilde{O}(T^{(d+1)/(d+2)})$ plus a $T$-independent coordination cost. This framework is significant as it extends to general distance-threshold collision models and provides a communication-free policy that maximizes collective reward. The authors' modular protocol first solves the multi-agent coordination problem and then decouples the problem into $N$ independent single-player Lipschitz bandits. This approach has potential applications in multi-agent systems, where coordination and communication can be costly and limited. However, the proposed protocol assumes a Lipschitz-structured action space, which might not be applicable to all multi-agent systems. Additionally, the coordination cost is $T$-independent, but the overall regret bound still depends on the time horizon $T$. Further research is needed to generalize the framework to more complex action spaces and reduce its dependence on $T$.
Recommendations
- ✓ Further research is needed to generalize the framework to more complex action spaces and reduce its dependence on $T$.
- ✓ The proposed protocol should be tested and evaluated in various multi-agent systems, including robotics, autonomous systems, and social networks, to demonstrate its effectiveness and applicability.
