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Lingda Wang

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4 papers

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AAAI Conference 2021 Conference Paper

Adversarial Linear Contextual Bandits with Graph-Structured Side Observations

Lingda Wang
Bingcong Li
Huozhi Zhou
Georgios B. Giannakis
Lav R. Varshney
Zhizhen Zhao

This paper studies the adversarial graphical contextual bandits, a variant of adversarial multi-armed bandits that leverage two categories of the most common side information: contexts and side observations. In this setting, a learning agent repeatedly chooses from a set of K actions after being presented with a d-dimensional context vector. The agent not only incurs and observes the loss of the chosen action, but also observes the losses of its neighboring actions in the observation structures, which are encoded as a series of feedback graphs. This setting models a variety of applications in social networks, where both contexts and graph-structured side observations are available. Two efficient algorithms are developed based on EXP3. Under mild conditions, our analysis shows that for undirected feedback graphs the first algorithm, EXP3-LGC-U, achieves a sub-linear regret with respect to the time horizon and the average independence number of the feedback graphs. A slightly weaker result is presented for the directed graph setting as well. The second algorithm, EXP3-LGC-IX, is developed for a special class of problems, for which the regret is the same for both directed as well as undirected feedback graphs. Numerical tests corroborate the efficiency of proposed algorithms.

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AAAI Conference 2021 Conference Paper

Enhancing Parameter-Free Frank Wolfe with an Extra Subproblem

Bingcong Li
Lingda Wang
Georgios B. Giannakis
Zhizhen Zhao

Aiming at convex optimization under structural constraints, this work introduces and analyzes a variant of the Frank Wolfe (FW) algorithm termed ExtraFW. The distinct feature of ExtraFW is the pair of gradients leveraged per iteration, thanks to which the decision variable is updated in a prediction-correction (PC) format. Relying on no problem dependent parameters in the step sizes, the convergence rate of ExtraFW for general convex problems is shown to be O( 1 k ), which is optimal in the sense of matching the lower bound on the number of solved FW subproblems. However, the merit of ExtraFW is its faster rate O 1 k2 on a class of machine learning problems. Compared with other parameter-free FW variants that have faster rates on the same problems, ExtraFW has improved rates and fine-grained analysis thanks to its PC update. Numerical tests on binary classification with different sparsity-promoting constraints demonstrate that the empirical performance of ExtraFW is significantly better than FW, and even faster than Nesterov’s accelerated gradient on certain datasets. For matrix completion, ExtraFW enjoys smaller optimality gap, and lower rank than FW.

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AAAI Conference 2020 Conference Paper

A Near-Optimal Change-Detection Based Algorithm for Piecewise-Stationary Combinatorial Semi-Bandits

Huozhi Zhou
Lingda Wang
Lav Varshney
Ee-Peng Lim

We investigate the piecewise-stationary combinatorial semibandit problem. Compared to the original combinatorial semi-bandit problem, our setting assumes the reward distributions of base arms may change in a piecewise-stationary manner at unknown time steps. We propose an algorithm, GLR-CUCB, which incorporates an efﬁcient combinatorial semi-bandit algorithm, CUCB, with an almost parameter-free change-point detector, the Generalized Likelihood Ratio Test (GLRT). Our analysis shows that the regret of GLR-CUCB is upper bounded by O( √ NKT log T), where N is the number of piecewise-stationary segments, K is the number of base arms, and T is the number of time steps. As a complement, we also derive a nearly matching regret lower bound on the order of Ω( √ NKT), for both piecewise-stationary multi-armed bandits and combinatorial semi-bandits, using information-theoretic techniques and judiciously constructed piecewise-stationary bandit instances. Our lower bound is tighter than the best available regret lower bound, which is Ω( √ T). Numerical experiments on both synthetic and realworld datasets demonstrate the superiority of GLR-CUCB compared to other state-of-the-art algorithms.

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ICML Conference 2020 Conference Paper

Almost Tune-Free Variance Reduction

Bingcong Li
Lingda Wang
Georgios B. Giannakis

The variance reduction class of algorithms including the representative ones, SVRG and SARAH, have well documented merits for empirical risk minimization problems. However, they require grid search to tune parameters (step size and the number of iterations per inner loop) for optimal performance. This work introduces ‘almost tune-free’ SVRG and SARAH schemes equipped with i) Barzilai-Borwein (BB) step sizes; ii) averaging; and, iii) the inner loop length adjusted to the BB step sizes. In particular, SVRG, SARAH, and their BB variants are first reexamined through an ‘estimate sequence’ lens to enable new averaging methods that tighten their convergence rates theoretically, and improve their performance empirically when the step size or the inner loop length is chosen large. Then a simple yet effective means to adjust the number of iterations per inner loop is developed to enhance the merits of the proposed averaging schemes and BB step sizes. Numerical tests corroborate the proposed methods.

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