In this work, we study the federated multi-armed bandit (FMAB) problem, where a set of agents collaboratively aim to minimize cumulative regret. Unlike traditional centralized bandit models, agents in FMAB settings are connected via a communication graph and cannot share data freely due to bandwidth limitations or privacy constraints. This raises a fundamental challenge: how to achieve optimal learning performance under stringent communication budgets. We propose a novel communication-efficient algorithm containing two points: one for eliminating suboptimal arms through early and frequent communication of key decisions, and the other for refining global estimates using incremental epoch, quantized, and differentially transmitted statistics. Incremental Epoch-based Successive Elimination Algorithm (EpoInc-SE) is presented by carefully balancing communication frequency and precision of global estimates. Theoretically, we derive tight upper bounds on both individual cumulative regret and group regret, and prove that our method asymptotically matches the lower bound of regret in federated settings.

We study the regret in stochastic Multi-Armed Bandits (MAB) with multiple agents that communicate over an arbitrary connected communication graph. We analyzed a variant of Cooperative Successive Elimination algorithm, Coop-SE, and show an individual regret bound of O(R/m+A2 +A logT) and a nearly matching lower bound. Here Ais the number of actions, T the time horizon, mthe number of agents, and R= P i>0 log(T)/ i is the optimal single agent regret, where i is the sub-optimality gap of action i. Our work is the first to show an individual regret bound in cooperative stochastic MAB that is independent of the graph's diameter. When considering communication networks there are additional considerations beyond regret, such as message size and number of communication rounds. First, we show that our regret bound holds even if we restrict the messages to be of logarithmic size. Second, for logarithmic number of communication rounds, we obtain a regret bound of O(R/m+AlogT).

We study the regret in stochastic Multi-Armed Bandits (MAB) with multiple agents that communicate over an arbitrary connected communication graph. We analyzed a variant of Cooperative Successive Elimination algorithm, $\texttt{Coop-SE}$, and show an individual regret bound of ${O}(\mathcal{R} / m + A^2 + A \sqrt{\log T})$ and a nearly matching lower bound. Here $A$ is the number of actions, $T$ the time horizon, $m$ the number of agents, and $\mathcal{R} = \sum_{\Delta_i > 0}\log(T)/\Delta_i$ is the optimal single agent regret, where $\Delta_i$ is the sub-optimality gap of action $i$. Our work is the first to show an individual regret bound in cooperative stochastic MAB that is independent of the graph's diameter. When considering communication networks there are additional considerations beyond regret, such as message size and number of communication rounds. First, we show that our regret bound holds even if we restrict the messages to be of logarithmic size. Second, for logarithmic number of communication rounds, we obtain a regret bound of ${O}(\mathcal{R} / m+A \log T)$.

Double Auction enables decentralized transfer of goods between multiple buyers and sellers, thus underpinning functioning of many online marketplaces. Buyers and sellers compete in these markets through bidding, but do not often know their own valuation a-priori. As the allocation and pricing happens through bids, the profitability of participants, hence sustainability of such markets, depends crucially on learning respective valuations through repeated interactions. We initiate the study of Double Auction markets under bandit feedback on both buyers' and sellers' side. We show with confidence bound based bidding, and'Average Pricing' there is an efficient price discovery among the participants.

Recent work on deriving O(log T) anytime regret bounds for stochastic dueling bandit problems has considered mostly Condorcet winners, which do not always exist, and more recently, winners defined by the Copeland set, which do always exist. In this work, we consider a broad notion of winners defined by tournament solutions in social choice theory, which include the Copeland set as a special case but also include several other notions of winners such as the top cycle, uncovered set, and Banks set, and which, like the Copeland set, always exist. We develop a family of UCB-style dueling bandit algorithms for such general tournament solutions, and show O(log T) anytime regret bounds for them. Experiments confirm the ability of our algorithms to achieve low regret relative to the target winning set of interest.

However, a theoretical understanding of their success in practice is still a mystery. Moreover, recent advances [34] on fast convergence in games are limited to no-regret algorithms such as online mirror descent, which satisfy stability.

Neural Information Processing Systems http://nips.cc/

We show with confidence bound based bidding, and'Average Pricing' there

We study agents communicating over an underlying network by exchanging messages, in order to optimize their individual regret in a common nonstochastic multi-armed bandit problem. We derive regret minimization algorithms that guarantee for each agent $v$ an individual expected regret of $\widetilde{O}\left(\sqrt{\left(1+\frac{K}{\left|\mathcal{N}\left(v\right)\right|}\right)T}\right)$, where $T$ is the number of time steps, $K$ is the number of actions and $\mathcal{N}\left(v\right)$ is the set of neighbors of agent $v$ in the communication graph. We present algorithms both for the case that the communication graph is known to all the agents, and for the case that the graph is unknown. When the graph is unknown, each agent knows only the set of its neighbors and an upper bound on the total number of agents. The individual regret between the models differs only by a logarithmic factor.