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1. Accelerated Spectral Ranking

   Agarwal, Arpit ; Patil, Prathamesh ; Agarwal, Shivani ( July 2018 , Proceedings of the 35th International Conference on Machine Learning, Proceedings of Machine Learning Research)

   The problem of rank aggregation from pairwise and multiway comparisons has a wide range of implications, ranging from recommendation systems to sports rankings to social choice. Some of the most popular algorithms for this problem come from the class of spectral ranking algorithms; these include the rank centrality (RC) algorithm for pairwise comparisons, which returns consistent estimates under the Bradley-Terry-Luce (BTL) model for pairwise comparisons (Negahban et al., 2017), and its generalization, the Luce spectral ranking (LSR) algorithm, which returns consistent estimates under the more general multinomial logit (MNL) model for multiway comparisons (Maystre & Grossglauser, 2015). In this paper, we design a provably faster spectral ranking algorithm, which we call accelerated spectral ranking (ASR), that is also consistent under the MNL/BTL models. Our accelerated algorithm is achieved by designing a random walk that has a faster mixing time than the random walks associated with previous algorithms. In addition to a faster algorithm, our results yield improved sample complexity bounds for recovery of the MNL/BTL parameters: to the best of our knowledge, we give the first general sample complexity bounds for recovering the parameters of the MNL model from multiway comparisons under any (connected) comparison graph (and improve significantly over previous bounds for the BTL model for pairwise comparisons). We also give a message-passing interpretation of our algorithm, which suggests a decentralized distributed implementation. Our experiments on several real-world and synthetic datasets confirm that our new ASR algorithm is indeed orders of magnitude faster than existing algorithms. 

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2. Accelerated Spectral Ranking

   Agarwal, Arpit ; Patil, Prathamesh ; Agarwal, Shivani ( January 2018 , Proceedings of the 35th International Conference on Machine Learning)

   The problem of rank aggregation from pairwise and multiway comparisons has a wide range of implications, ranging from recommendation systems to sports rankings to social choice. Some of the most popular algorithms for this problem come from the class of spectral ranking algorithms; these include the rank centrality (RC) algorithm for pairwise comparisons, which returns consistent estimates under the Bradley-Terry-Luce (BTL) model for pairwise comparisons (Negahban et al., 2017), and its generalization, the Luce spectral ranking (LSR) algorithm, which returns consistent estimates under the more general multinomial logit (MNL) model for multiway comparisons (Maystre & Grossglauser, 2015). In this paper, we design a provably faster spectral ranking algorithm, which we call accelerated spectral ranking (ASR), that is also consistent under the MNL/BTL models. Our accelerated algorithm is achieved by designing a random walk that has a faster mixing time than the random walks associated with previous algorithms. In addition to a faster algorithm, our results yield improved sample complexity bounds for recovery of the MNL/BTL parameters: to the best of our knowledge, we give the first general sample complexity bounds for recovering the parameters of the MNL model from multiway comparisons under any (connected) comparison graph (and improve significantly over previous bounds for the BTL model for pairwise comparisons). We also give a message-passing interpretation of our algorithm, which suggests a decentralized distributed implementation. Our experiments on several real-world and synthetic datasets confirm that our new ASR algorithm is indeed orders of magnitude faster than existing algorithms. 

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3. Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons

   Zhu, Banghua and ( January 2023 , Proceedings of Machine Learning Research)

   Krause, Andreas and (Ed.)

   We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). We show that when the underlying true reward is linear, under both Bradley-Terry-Luce (BTL) model (pairwise comparison) and Plackett-Luce (PL) model ($K$-wise comparison), MLE converges under certain semi-norm for the family of linear reward. On the other hand, when training a policy based on the learned reward model, we show that MLE fails while a pessimistic MLE provides policies with good performance under certain coverage assumption. We also show that under the PL model, both the true MLE and a different MLE which splits the $K$-wise comparison into pairwise comparisons converge, while the true MLE is asymptotically more efficient. Our results validate the empirical success of the existing RLHF algorithms, and provide new insights for algorithm design. Our analysis can also be applied for the problem of online RLHF and inverse reinforcement learning. 

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4. Adversarial Bandits with Corruptions

   Yang, Lin ; Hajiesmaili, Mohammad H ; Talebi, Mohammad Sadegh ; Lui, John C ; Wong, Wing Shing ( December 2020 , Advances in Neural Information Processing Systems 33 (NeurIPS 2020))

   null (Ed.)

   This paper studies adversarial bandits with corruptions. In the basic adversarial bandit setting, the reward of arms is predetermined by an adversary who is oblivious to the learner’s policy. In this paper, we consider an extended setting in which an attacker sits in-between the environment and the learner, and is endowed with a limited budget to corrupt the reward of the selected arm. We have two main results. First, we derive a lower bound on the regret of any bandit algorithm that is aware of the budget of the attacker. Also, for budget-agnostic algorithms, we characterize an impossibility result demonstrating that even when the attacker has a sublinear budget, i.e., a budget growing sublinearly with time horizon T, they fail to achieve a sublinear regret. Second, we propose ExpRb, a bandit algorithm that incorporates a biased estimator and a robustness parameter to deal with corruption. We characterize the regret of ExpRb as a function of the corruption budget and show that for the case of a known corruption budget, the regret of ExpRb is tight. 

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5. The White-Box Adversarial Data Stream Model

   https://doi.org/10.1145/3517804.3526228  

   Ajtai, M. ; Braverman, V. ; Jayram, T.S. ; Silwal, S. ; Sun, A. ; Woodruff, D.P. ; Zhou, S. ( January 2022 , Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS 2022))

   There has been a flurry of recent literature studying streaming algorithms for which the input stream is chosen adaptively by a black-box adversary who observes the output of the streaming algorithm at each time step. However, these algorithms fail when the adversary has access to the internal state of the algorithm, rather than just the output of the algorithm. We study streaming algorithms in the white-box adversarial model, where the stream is chosen adaptively by an adversary who observes the entire internal state of the algorithm at each time step. We show that nontrivial algorithms are still possible. We first give a randomized algorithm for the L1-heavy hitters problem that outperforms the optimal deterministic Misra-Gries algorithm on long streams. If the white-box adversary is computationally bounded, we use cryptographic techniques to reduce the memory of our L1-heavy hitters algorithm even further and to design a number of additional algorithms for graph, string, and linear algebra problems. The existence of such algorithms is surprising, as the streaming algorithm does not even have a secret key in this model, i.e., its state is entirely known to the adversary. One algorithm we design is for estimating the number of distinct elements in a stream with insertions and deletions achieving a multiplicative approximation and sublinear space; such an algorithm is impossible for deterministic algorithms. We also give a general technique that translates any two-player deterministic communication lower bound to a lower bound for randomized algorithms robust to a white-box adversary. In particular, our results show that for all p ≥ 0, there exists a constant Cp > 1 such that any Cp-approximation algorithm for Fp moment estimation in insertion-only streams with a white-box adversary requires Ω(n) space for a universe of size n. Similarly, there is a constant C > 1 such that any C-approximation algorithm in an insertion-only stream for matrix rank requires Ω(n) space with a white-box adversary. These results do not contradict our upper bounds since they assume the adversary has unbounded computational power. Our algorithmic results based on cryptography thus show a separation between computationally bounded and unbounded adversaries. Finally, we prove a lower bound of Ω(log n) bits for the fundamental problem of deterministic approximate counting in a stream of 0’s and 1’s, which holds even if we know how many total stream updates we have seen so far at each point in the stream. Such a lower bound for approximate counting with additional information was previously unknown, and in our context, it shows a separation between multiplayer deterministic maximum communication and the white-box space complexity of a streaming algorithm 

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