We show that several online combinatorial optimization problems that admit efficient no-regret algorithms become computationally hard in the sleeping setting where a subset of actions becomes unavailable in each round. Specifically, we show that the sleeping versions of these problems are at least as hard as PAC learning DNF expressions, a long standing open problem.

Subgraph-based methods have proven to be effective and interpretable in predicting drug-drug interactions (DDIs), which are essential for medical practice and drug development. Subgraph selection and encoding are critical stages in these methods, yet customizing these components remains underexplored due to the high cost of manual adjustments. In this study, inspired by the success of neural architecture search (NAS), we propose a method to search for data-specific components within subgraph-based frameworks. Specifically, we introduce extensive subgraph selection and encoding spaces that account for the diverse contexts of drug interactions in DDI prediction. To address the challenge of large search spaces and high sampling costs, we design a relaxation mechanism that uses an approximation strategy to efficiently explore optimal subgraph configurations. This approach allows for robust exploration of the search space. Extensive experiments demonstrate the effectiveness and superiority of the proposed method, with the discovered subgraphs and encoding functions highlighting the model's adaptability.

In this paper, we study the contextual multinomial logistic (MNL) bandit problem in which a learning agent sequentially selects an assortment based on contextual information, and user feedback follows an MNL choice model. There has been a significant discrepancy between lower and upper regret bounds, particularly regarding the maximum assortment size K. Additionally, the variation in reward structures between these bounds complicates the quest for optimality. Under uniform rewards, where all items have the same expected reward, we establish a regret lower bound of Ωpd? T {Kq and propose a constant-time algorithm, OFU-MNL+, that achieves a matching upper bound of Õpd? T {Kq. We also provide instancedependent minimax regret bounds under uniform rewards. Under non-uniform rewards, we prove a lower bound of Ωpd? T q and an upper bound of Õpd? T q, also achievable by OFU-MNL+. Our empirical studies support these theoretical findings. To the best of our knowledge, this is the first work in the contextual MNL bandit literature to prove minimax optimality -- for either uniform or non-uniform reward setting -- and to propose a computationally efficient algorithm that achieves this optimality up to logarithmic factors.

For constrained, not necessarily monotone submodular maximization, all known approximation algorithms with ratio greater than 1/e require continuous ideas, such as queries to the multilinear extension of a submodular function and its gradient, which are typically expensive to simulate with the original set function. For combinatorial algorithms, the best known approximation ratios for both size and matroid constraint are obtained by a simple randomized greedy algorithm of Buchbinder et al. [9]: 1/e 0.367 for size constraint and 0.281 for the matroid constraint in O(kn) queries, where k is the rank of the matroid. In this work, we develop the first combinatorial algorithms to break the 1/e barrier: we obtain approximation ratio of 0.385 in O(kn) queries to the submodular set function for size constraint, and 0.305 for a general matroid constraint. These are achieved by guiding the randomized greedy algorithm with a fast local search algorithm. Further, we develop deterministic versions of these algorithms, maintaining the same ratio and asymptotic time complexity. Finally, we develop a deterministic, nearly linear time algorithm with ratio 0.377.

Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of M 2 random variables. Probably the most widespread independence measure relying on kernels is the socalled Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades ago, the fundamental question of the rate at which HSIC can be estimated is still open.

This work proposes a self-supervised training strategy designed for combinatorial problems. An obstacle in applying supervised paradigms to such problems is the need for costly target solutions often produced with exact solvers. Inspired by semi-and self-supervised learning, we show that generative models can be trained by sampling multiple solutions and using the best one according to the problem objective as a pseudo-label. In this way, we iteratively improve the model generation capability by relying only on its self-supervision, eliminating the need for optimality information. We validate this Self-Labeling Improvement Method (SLIM) on the Job Shop Scheduling (JSP), a complex combinatorial problem that is receiving much attention from the neural combinatorial community. We propose a generative model based on the well-known Pointer Network and train it with SLIM. Experiments on popular benchmarks demonstrate the potential of this approach as the resulting models outperform constructive heuristics and state-of-the-art learning proposals for the JSP. Lastly, we prove the robustness of SLIM to various parameters and its generality by applying it to the Traveling Salesman Problem.

This paper aims at the third, i.e., developing the Sampling-exploration enhanced A

A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size n subject to cardinality constraint k; the algorithm is based upon the idea of interlacing two greedy procedures.

The state-of-the-art approximate nearest neighbor search (ANNS) algorithm builds a large proximity graph on the dataset and performs a greedy beam search, which may bring many unnecessary explorations. We develop a novel framework, namely corssing sparse proximity graph (CSPG), based on random partitioning of the dataset. It produces a smaller sparse proximity graph for each partition and routing vectors that bind all the partitions. An efficient two-staged approach is designed for exploring CSPG, with fast approaching and cross-partition expansion. We theoretically prove that CSPG can accelerate the existing graph-based ANNS algorithms by reducing unnecessary explorations. In addition, we conduct extensive experiments on benchmark datasets. The experimental results confirm that the existing graph-based methods can be significantly outperformed by incorporating CSPG, achieving 1.5x to 2x speedups of QPS in almost all recalls.

Optimization of convex functions under stochastic zeroth-order feedback has been a major and challenging question in online learning. In this work, we consider the problem of optimizing second-order smooth and strongly convex functions where the algorithm is only accessible to noisy evaluations of the objective function it queries. We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds. We propose an algorithm that features a combination of a bootstrapping stage and a mirror-descent stage. Our main technical innovation consists of a sharp characterization for the spherical-sampling gradient estimator under higher-order smoothness conditions, which allows the algorithm to optimally balance the bias-variance tradeoff, and a new iterative method for the bootstrapping stage, which maintains the performance for unbounded Hessian.