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We study the multi-agent multi-armed bandit (MAMAB) problem, where agents are factored into overlapping groups. Each group represents a hyperedge, forming a hypergraph over the agents. At each round of interaction, the learner pulls a joint arm (composed of individual arms for each agent) and receives a reward according to the hypergraph structure. Specifically, we assume there is a local reward for each hyperedge, and the reward of the joint arm is the sum of these local rewards. Previous work introduced the multi-agent Thompson sampling (MATS) algorithm and derived a Bayesian regret bound. However, it remains an open problem how to derive a frequentist regret bound for Thompson sampling in this multi-agent setting. To address these issues, we propose an efficient variant of MATS, the epsilon-exploring Multi-Agent Thompson Sampling (eps-MATS) algorithm, which performs MATS exploration with probability epsilon while adopts a greedy policy otherwise. We prove that eps-MATS achieves a worst-case frequentist regret bound that is sublinear in both the time horizon and the local arm size. We also derive a lower bound for this setting, which implies our frequentist regret upper bound is optimal up to constant and logarithm terms, when the hypergraph is sufficiently sparse. Thorough experiments on standard MAMAB problems demonstrate the superior performance and the improved computational efficiency of eps-MATS compared with existing algorithms in the same setting.
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A Scenario Approach to Robust Simulation-based Path Planning
We consider a prototypical path planning problem on a graph with uncertain cost of mobility on its edges. At a given node, the planning agent can access the true cost for edges to its neighbors and uses a noisy simulator to estimate the cost-to-go from the neighboring nodes. The objective of the planning agent is to select a neighboring node such that, with high probability, the cost-to-go is minimized for the worst possible realization of uncertain parameters in the simulator. By modeling the cost-to-go as a Gaussian process (GP) for every realization of the uncertain parameters, we apply a scenario approach in which we draw fixed independent samples of the uncertain parameter. We present a scenario-based iterative algorithm using the upper confidence bound (UCB) of the fixed independent scenarios to compute the choice of the neighbor to go to. We characterize the performance of the proposed algorithm in terms of a novel notion of regret defined with respect to an additional draw of the uncertain parameter, termed as scenario regret under re-draw. In particular, we characterize a high probability upper bound on the regret under re-draw for any finite number of iterations of the algorithm, and show that this upper bound tends to zero asymptotically with the number of iterations. We supplement our analysis with numerical results.
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- PAR ID:
- 10346597
- Date Published:
- Journal Name:
- Proceedings of the American Control Conference
- ISSN:
- 0743-1619
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC53348.2022.9867194
