skip to main content

Title: Multi-Agent Multi-Armed Bandits with Limited Communication
We consider the problem where N agents collaboratively interact with an instance of a stochastic K arm bandit problem for K N. The agents aim to simultaneously minimize the cumulative regret over all the agents for a total of T time steps, the number of communication rounds, and the number of bits in each communication round. We present Limited Communication Collaboration - Upper Confidence Bound (LCC-UCB), a doubling-epoch based algorithm where each agent communicates only after the end of the epoch and shares the index of the best arm it knows. With our algorithm, LCC-UCB, each agent enjoys a regret of O√(K/N + N)T, communicates for O(log T) steps and broadcasts O(log K) bits in each communication step. We extend the work to sparse graphs with maximum degree KG and diameter D to propose LCC-UCB-GRAPH which enjoys a regret bound of O√(D(K/N + KG)DT). Finally, we empirically show that the LCC-UCB and the LCC-UCB-GRAPH algorithms perform well and outperform strategies that communicate through a central node.  more » « less
Award ID(s):
Author(s) / Creator(s):
Date Published:
Journal Name:
Journal of machine learning research
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    In this paper, we study Federated Bandit, a decentralized Multi-Armed Bandit problem with a set of N agents, who can only communicate their local data with neighbors described by a connected graph G. Each agent makes a sequence of decisions on selecting an arm from M candidates, yet they only have access to local and potentially biased feedback/evaluation of the true reward for each action taken. Learning only locally will lead agents to sub-optimal actions while converging to a no-regret strategy requires a collection of distributed data. Motivated by the proposal of federated learning, we aim for a solution with which agents will never share their local observations with a central entity, and will be allowed to only share a private copy of his/her own information with their neighbors. We first propose a decentralized bandit algorithm \textttGossip\_UCB, which is a coupling of variants of both the classical gossiping algorithm and the celebrated Upper Confidence Bound (UCB) bandit algorithm. We show that \textttGossip\_UCB successfully adapts local bandit learning into a global gossiping process for sharing information among connected agents, and achieves guaranteed regret at the order of O(\max\ \textttpoly (N,M) łog T, \textttpoly (N,M)łog_łambda_2^-1 N\ ) for all N agents, where łambda_2\in(0,1) is the second largest eigenvalue of the expected gossip matrix, which is a function of G. We then propose \textttFed\_UCB, a differentially private version of \textttGossip\_UCB, in which the agents preserve ε-differential privacy of their local data while achieving O(\max \\frac\textttpoly (N,M) ε łog^2.5 T, \textttpoly (N,M) (łog_łambda_2^-1 N + łog T) \ ) regret. 
    more » « less
  2. We consider a multi-agent multi-armed bandit setting in which n honest agents collaborate over a network to minimize regret but m malicious agents can disrupt learning arbitrarily. Assuming the network is the complete graph, existing algorithms incur O((m + K/n) łog (T) / Δ ) regret in this setting, where K is the number of arms and Δ is the arm gap. For m łl K, this improves over the single-agent baseline regret of O(Kłog(T)/Δ). In this work, we show the situation is murkier beyond the case of a complete graph. In particular, we prove that if the state-of-the-art algorithm is used on the undirected line graph, honest agents can suffer (nearly) linear regret until time is doubly exponential in K and n . In light of this negative result, we propose a new algorithm for which the i -th agent has regret O(( dmal (i) + K/n) łog(T)/Δ) on any connected and undirected graph, where dmal(i) is the number of i 's neighbors who are malicious. Thus, we generalize existing regret bounds beyond the complete graph (where dmal(i) = m), and show the effect of malicious agents is entirely local (in the sense that only the dmal (i) malicious agents directly connected to i affect its long-term regret). 
    more » « less
  3. null (Ed.)
    Federated multi-armed bandits (FMAB) is a new bandit paradigm that parallels the federated learning (FL) framework in supervised learning. It is inspired by practical applications in cognitive radio and recommender systems, and enjoys features that are analogous to FL. This paper proposes a general framework of FMAB and then studies two specific federated bandit models. We first study the approximate model where the heterogeneous local models are random realizations of the global model from an unknown distribution. This model introduces a new uncertainty of client sampling, as the global model may not be reliably learned even if the finite local models are perfectly known. Furthermore, this uncertainty cannot be quantified a priori without knowledge of the suboptimality gap. We solve the approximate model by proposing Federated Double UCB (Fed2-UCB), which constructs a novel “double UCB” principle accounting for uncertainties from both arm and client sampling. We show that gradually admitting new clients is critical in achieving an O(log(T)) regret while explicitly considering the communication loss. The exact model, where the global bandit model is the exact average of heterogeneous local models, is then studied as a special case. We show that, somewhat surprisingly, the order-optimal regret can be achieved independent of the number of clients with a careful choice of the update periodicity. Experiments using both synthetic and real-world datasets corroborate the theoretical analysis and demonstrate the effectiveness and efficiency of the proposed algorithms. 
    more » « less
  4. We investigate robust data aggregation in a multi-agent online learning setting. In reality, multiple online learning agents are often deployed to perform similar tasks and receive similar feedback. We study how agents can improve their collective performance by sharing information among each other. In this paper, we formulate the ε-multi-player multi-armed bandit problem, in which a set of M players that have similar reward distributions for each arm play concurrently. We develop an upper confidence bound-based algorithm that adaptively aggregates rewards collected by different players. To our best knowledge, we are the first to develop such a scheme in a multi-player bandit learning setting. We show that under the assumption that pairwise distances between the means of the player-dependent distributions for each arm are small, we improve the (collective) regret bound by nearly a factor of M , in comparison with a baseline algorithm in which the players learn individually using the UCB-1 algorithm (Auer et al., 2002). Our algorithm also exhibits a fallback guarantee, namely, if our task similarity assumption fails to hold, our algorithm still has a performance guarantee that cannot be worse than the baseline by a constant factor. Empirically, we validate our algorithm on synthetic data. 
    more » « less
  5. We study model-free reinforcement learning (RL) algorithms for infinite-horizon average-reward Markov decision process (MDP), which is more appropriate for applications that involve continuing operations not divided into episodes. In contrast to episodic/discounted MDPs, theoretical understanding of model-free RL algorithms is relatively inadequate for the average-reward setting. In this paper, we consider both the online setting and the setting with access to a simulator. We develop computationally efficient model-free algorithms that achieve sharper guarantees on regret/sample complexity compared with existing results. In the online setting, we design an algorithm, UCB-AVG, based on an optimistic variant of variance-reduced Q-learning. We show that UCB-AVG achieves a regret bound $\widetilde{O}(S^5A^2sp(h^*)\sqrt{T})$ after $T$ steps, where $S\times A$ is the size of state-action space, and $sp(h^*)$ the span of the optimal bias function. Our result provides the first computationally efficient model-free algorithm that achieves the optimal dependence in $T$ (up to log factors) for weakly communicating MDPs, which is necessary for low regret. In contrast, prior results either are suboptimal in $T$ or require strong assumptions of ergodicity or uniformly mixing of MDPs. In the simulator setting, we adapt the idea of UCB-AVG to develop a model-free algorithm that finds an $\epsilon$-optimal policy with sample complexity $\widetilde{O}(SAsp^2(h^*)\epsilon^{-2} + S^2Asp(h^*)\epsilon^{-1}).$ This sample complexity is near-optimal for weakly communicating MDPs, in view of the minimax lower bound $\Omega(SAsp(^*)\epsilon^{-2})$. Existing work mainly focuses on ergodic MDPs and the results typically depend on $t_{mix},$ the worst-case mixing time induced by a policy. We remark that the diameter $D$ and mixing time $t_{mix}$ are both lower bounded by $sp(h^*)$, and $t_{mix}$ can be arbitrarily large for certain MDPs. On the technical side, our approach integrates two key ideas: learning an $\gamma$-discounted MDP as an approximation, and leveraging reference-advantage decomposition for variance in optimistic Q-learning. As recognized in prior work, a naive approximation by discounted MDPs results in suboptimal guarantees. A distinguishing feature of our method is maintaining estimates of value-difference between state pairs to provide a sharper bound on the variance of reference advantage. We also crucially use a careful choice of the discounted factor $\gamma$ to balance approximation error due to discounting and the statistical learning error, and we are able to maintain a good-quality reference value function with $O(SA)$ space complexity. 
    more » « less