An official website of the United States government
In many real-world applications, multiple agents seek to learn how to perform highly related yet slightly different tasks in an online bandit learning protocol. We formulate this problem as the ϵ-multi-player multi-armed bandit problem, in which a set of players concurrently interact with a set of arms, and for each arm, the reward distributions for all players are similar but not necessarily identical. We develop an upper confidence bound-based algorithm, RobustAgg(ϵ), that adaptively aggregates rewards collected by different players. In the setting where an upper bound on the pairwise dissimilarities of reward distributions between players is known, we achieve instance-dependent regret guarantees that depend on the amenability of information sharing across players. We complement these upper bounds with nearly matching lower bounds. In the setting where pairwise dissimilarities are unknown, we provide a lower bound, as well as an algorithm that trades off minimax regret guarantees for adaptivity to unknown similarity structure.
more »
« less
Distributed No-Regret Learning for Multi-Stage Systems with End-to-End Bandit Feedback
This paper studies multi-stage systems with end-to-end bandit feedback. In such systems, each job needs to go through multiple stages, each managed by a different agent, before generating an outcome. Each agent can only control its own action and learn the final outcome of the job. It has neither knowledge nor control on actions taken by agents in the next stage. The goal of this paper is to develop distributed online learning algorithms that achieve sublinear regret in adversarial environments. The setting of this paper significantly expands the traditional multi-armed bandit problem, which considers only one agent and one stage. In addition to the exploration-exploitation dilemma in the traditional multi-armed bandit problem, we show that the consideration of multiple stages introduces a third component, education, where an agent needs to choose its actions to facilitate the learning of agents in the next stage. To solve this newly introduced exploration-exploitation-education trilemma, we propose a simple distributed online learning algorithm, ϵ-EXP3. We theoretically prove that the ϵ-EXP3 algorithm is a no-regret policy that achieves sublinear regret. Simulation results show that the ϵ-EXP3 algorithm significantly outperforms existing no-regret online learning algorithms for the traditional multi-armed bandit problem.
more »
« less
- PAR ID:
- 10600088
- Publisher / Repository:
- ACM
- Date Published:
- ISBN:
- 9798400705212
- Page Range / eLocation ID:
- 41 to 50
- Format(s):
- Medium: X
- Location:
- Athens Greece
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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.more » « less
-
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.more » « less
-
null (Ed.)In multi-server queueing systems where there is no central queue holding all incoming jobs, job dispatching policies are used to assign incoming jobs to the queue at one of the servers. Classic job dispatching policies such as join-the-shortest-queue and shortest expected delay assume that the service rates and queue lengths of the servers are known to the dispatcher. In this work, we tackle the problem of job dispatching without the knowledge of service rates and queue lengths, where the dispatcher can only obtain noisy estimates of the service rates by observing job departures. This problem presents a novel exploration-exploitation trade-off between sending jobs to all the servers to estimate their service rates, and exploiting the currently known fastest servers to minimize the expected queueing delay. We propose a bandit-based exploration policy that learns the service rates from observed job departures. Unlike the standard multi-armed bandit problem where only one out of a finite set of actions is optimal, here the optimal policy requires identifying the optimal fraction of incoming jobs to be sent to each server. We present a regret analysis and simulations to demonstrate the effectiveness of the proposed bandit-based exploration policy.more » « less
-
We propose and evaluate a learning-based framework to address multi-agent resource allocation in coupled wireless systems. In particular we consider, multiple agents (e.g., base stations, access points, etc.) that choose amongst a set of resource allocation options towards achieving their own performance objective /requirements, and where the performance observed at each agent is further coupled with the actions chosen by the other agents, e.g., through interference, channel leakage, etc. The challenge is to find the best collective action. To that end we propose a Multi-Armed Bandit (MAB) framework wherein the best actions (aka arms) are adaptively learned through online reward feedback. Our focus is on systems which are "weakly-coupled" wherein the best arm of each agent is invariant to others' arm selection the majority of the time - this majority structure enables one to develop light weight efficient algorithms. This structure is commonly found in many wireless settings such as channel selection and power control. We develop a bandit algorithm based on the Track-and-Stop strategy, which shows a logarithmic regret with respect to a genie. Finally through simulation, we exhibit the potential use of our model and algorithm in several wireless application scenarios.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3641512.3686369
