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1. DART: Adaptive Accept Reject Algorithm for Non-Linear Combinatorial Bandits

   Agarwal, Mridul ; Aggarwal, Vaneet ; Umrawal, Abhishek K. ; Quinn, Christopher J. ( May 2021 , Proceedings of the AAAI Conference on Artificial Intelligence)

   We consider the bandit problem of selecting K out of N arms at each time step. The joint reward can be a non-linear function of the rewards of the selected individual arms. The direct use of a multi-armed bandit algorithm requires choosing among all possible combinations, making the action space large. To simplify the problem, existing works on combinatorial bandits typically assume feedback as a linear function of individual rewards. In this paper, we prove the lower bound for top-K subset selection with bandit feedback with possibly correlated rewards. We present a novel algorithm for the combinatorial setting without using individual arm feedback or requiring linearity of the reward function. Additionally, our algorithm works on correlated rewards of individual arms. Our algorithm, aDaptive Accept RejecT (DART), sequentially finds good arms and eliminates bad arms based on confidence bounds. DART is computationally efficient and uses storage linear in N. Further, DART achieves a regret bound of Õ(K√KNT) for a time horizon T, which matches the lower bound in bandit feedback up to a factor of √log 2NT. When applied to the problem of cross-selling optimization and maximizing the mean of individual rewards, the performance of the proposed algorithm surpasses that ofmore »state-of-the-art algorithms. We also show that DART significantly outperforms existing methods for both linear and non-linear joint reward environments.« less
2. An explore-then-commit algorithm for submodular maximization under full-bandit feedback

   Nie, Guanyu ; Agarwal, Mridul ; Umrawal, Abhishek Kumar ; Aggarwal, Vaneet ; Quinn, Christopher John ( January 2022 , Uncertainty in Artificial Intelligence)

   Cussens, James ; Zhang, Kun (Ed.)

   We investigate the problem of combinatorial multi-armed bandits with stochastic submodular (in expectation) rewards and full-bandit feedback, where no extra information other than the reward of selected action at each time step $t$ is observed. We propose a simple algorithm, Explore-Then-Commit Greedy (ETCG) and prove that it achieves a $(1-1/e)$-regret upper bound of $\mathcal{O}(n^\frac{1}{3}k^\frac{4}{3}T^\frac{2}{3}\log(T)^\frac{1}{2})$ for a horizon $T$, number of base elements $n$, and cardinality constraint $k$. We also show in experiments with synthetic and real-world data that the ETCG empirically outperforms other full-bandit methods.
3. Randomized Greedy Learning for Non-monotone Stochastic Submodular Maximization Under Full-bandit Feedback

   Fourati, Fares ; Aggarwal, Vaneet ; Quinn, Christopher John ; Alouini, Mohamed-Slim ( January 2023 , Proceedings of the International Workshop on Artificial Intelligence and Statistics)

   We investigate the problem of unconstrained combinatorial multi-armed bandits with full-bandit feedback and stochastic rewards for submodular maximization. Previous works investigate the same problem assuming a submodular and monotone reward function. In this work, we study a more general problem, i.e., when the reward function is not necessarily monotone, and the submodularity is assumed only in expectation. We propose Randomized Greedy Learning (RGL) algorithm and theoretically prove that it achieves a $\frac{1}{2}$-regret upper bound of $\Tilde{\mathcal{O}}(n T^{\frac{2}{3}})$ for horizon $T$ and number of arms $n$. We also show in experiments that RGL empirically outperforms other full-bandit variants in submodular and non-submodular settings.
4. Robust Multi-Agent Bandits Over Undirected Graphs

   https://doi.org/10.1145/3570614  

   Vial, Daniel ; Shakkottai, Sanjay ; Srikant, R. ( December 2022 , Proceedings of the ACM on Measurement and Analysis of Computing Systems)

   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) maliciousmore »agents directly connected to i affect its long-term regret).« less
5. Randomized Greedy Learning for Non-monotone Stochastic Submodular Maximization Under Full-bandit Feedback

   Fares Fourati, Vaneet Aggarwal ( January 2023 , Proceedings of Machine Learning Research)

   We investigate the problem of unconstrained combinatorial multi-armed bandits with fullbandit feedback and stochastic rewards for submodular maximization. Previous works investigate the same problem assuming a submodular and monotone reward function. In this work, we study a more general problem, i.e., when the reward function is not necessarily monotone, and the submodularity is assumed only in expectation. We propose Randomized Greedy Learning (RGL) algorithm and theoretically prove that it achieves a 1 2 -regret upper bound of O˜(nT 2 3 ) for horizon T and number of arms n. We also show in experiments that RGL empirically outperforms other full-bandit variants in submodular and non-submodular settings.