Yingkai Li

Matteo Castiglioni, Junjie Chen, Yingkai Li

We initiate the algorithmic study of fair contract design. A principal assigns multiple tasks to heterogeneous agents and chooses task-level linear contracts; agents differ in costs and success probabilities, and fairness requires each agent to prefer her own task-contract bundle to any other agent's. Unlike envy-free allocations of indivisible items, envy-free full-allocation contracts always exist, but optimizing revenue under this constraint is computationally difficult: no polynomial-time algorithm can achieve any constant-factor approximation in general. We therefore identify tractable regimes. With a constant number of tasks, optimal EF, EF1, and $ε$-EF contracts are computable in polynomial time. With a constant number of agents, exact EF remains hard, even for three agents, while EF1 and $ε$-EF admit additive FPTAS against the EF benchmark. We also show that exact EF can have an unbounded price of fairness, whereas $ε$-EF and EF1 can restore bounded revenue loss.

Xinxiang Guo, Yingkai Li, Yifen Mu

Decision-makers often rely on multiple probabilistic forecasts that are individually calibrated but need not be fully informative. We develop a framework for aggregating such forecasts when the decision-maker knows only that experts satisfy calibration. We show that the joint distribution of calibrated forecasts can contain decision-relevant information that is unavailable from any single expert, so the standard optimal-in-hindsight (OIH) benchmark may substantially understate attainable performance. To formalize this idea, we introduce a robust max-min benchmark: the best payoff a decision-maker can guarantee against all profile-wise conditional-mean mappings compatible with calibration. This benchmark is tractable, admits a linear-programming formulation, and dominates the OIH benchmark up to calibration error. It can nevertheless be strictly below the Bayesian benchmark, clarifying the value of knowing experts' information structures. Finally, we provide online algorithms that attain the robust benchmark under forecast-only feedback and stronger contextual benchmarks under state feedback.

Kefan Dong, Yingkai Li, Qin Zhang et al.

We study multinomial logit bandit with limited adaptivity, where the algorithms change their exploration actions as infrequently as possible when achieving almost optimal minimax regret. We propose two measures of adaptivity: the assortment switching cost and the more fine-grained item switching cost. We present an anytime algorithm (AT-DUCB) with $O(N \log T)$ assortment switches, almost matching the lower bound $Ω(\frac{N \log T}{ \log \log T})$. In the fixed-horizon setting, our algorithm FH-DUCB incurs $O(N \log \log T)$ assortment switches, matching the asymptotic lower bound. We also present the ESUCB algorithm with item switching cost $O(N \log^2 T)$.

Yingkai Li, Edmund Y. Lou, Liren Shan

We extend the model of stochastic bandits with adversarial corruption (Lykouriset al., 2018) to the stochastic linear optimization problem (Dani et al., 2008). Our algorithm is agnostic to the amount of corruption chosen by the adaptive adversary. The regret of the algorithm only increases linearly in the amount of corruption. Our algorithm involves using Löwner-John's ellipsoid for exploration and dividing time horizon into epochs with exponentially increasing size to limit the influence of corruption.

Yingkai Li, Yining Wang, Xi Chen et al.

Linear contextual bandit is an important class of sequential decision making problems with a wide range of applications to recommender systems, online advertising, healthcare, and many other machine learning related tasks. While there is a lot of prior research, tight regret bounds of linear contextual bandit with infinite action sets remain open. In this paper, we address this open problem by considering the linear contextual bandit with (changing) infinite action sets. We prove a regret upper bound on the order of $O(\sqrt{d^2T\log T})\times \text{poly}(\log\log T)$ where $d$ is the domain dimension and $T$ is the time horizon. Our upper bound matches the previous lower bound of $Ω(\sqrt{d^2 T\log T})$ in [Li et al., 2019] up to iterated logarithmic terms.

Yingkai Li, Yining Wang, Yuan Zhou

We study the linear contextual bandit problem with finite action sets. When the problem dimension is $d$, the time horizon is $T$, and there are $n \leq 2^{d/2}$ candidate actions per time period, we (1) show that the minimax expected regret is $Ω(\sqrt{dT (\log T) (\log n)})$ for every algorithm, and (2) introduce a Variable-Confidence-Level (VCL) SupLinUCB algorithm whose regret matches the lower bound up to iterated logarithmic factors. Our algorithmic result saves two $\sqrt{\log T}$ factors from previous analysis, and our information-theoretical lower bound also improves previous results by one $\sqrt{\log T}$ factor, revealing a regret scaling quite different from classical multi-armed bandits in which no logarithmic $T$ term is present in minimax regret. Our proof techniques include variable confidence levels and a careful analysis of layer sizes of SupLinUCB on the upper bound side, and delicately constructed adversarial sequences showing the tightness of elliptical potential lemmas on the lower bound side.

Yingkai Li, Huidong Liu

In this paper, we implement the Stochastic Damped LBFGS (SdLBFGS) for stochastic non-convex optimization. We make two important modifications to the original SdLBFGS algorithm. First, by initializing the Hessian at each step using an identity matrix, the algorithm converges better than original algorithm. Second, by performing direction normalization we could gain stable optimization procedure without line search. Experiments on minimizing a 2D non-convex function shows that our improved algorithm converges better than original algorithm, and experiments on the CIFAR10 and MNIST datasets show that our improved algorithm works stably and gives comparable or even better testing accuracies than first order optimizers SGD, Adagrad, and second order optimizers LBFGS in PyTorch.