We consider a finite-horizon multi-armed bandit (MAB) problem in a Bayesian setting, for which we propose an information relaxation sampling framework. With this framework, we define an intuitive family of control policies that include Thompson sampling (TS) and the Bayesian optimal policy as endpoints. Analogous to TS, which, at each decision epoch pulls an arm that is best with respect to the randomly sampled parameters, our algorithms sample entire future reward realizations and take the corresponding best action. However, this is done in the presence of "penalties" that seek to compensate for the availability of future information. We develop several novel policies and performance bounds for MAB problems that vary in terms of improving performance and increasing computational complexity between the two endpoints. Our policies can be viewed as natural generalizations of TS that simultaneously incorporate knowledge of the time horizon and explicitly consider the exploration-exploitation trade-off. We prove associated structural results on performance bounds and suboptimality gaps. Numerical experiments suggest that this new class of policies perform well, in particular in settings where the finite time horizon introduces significant exploration-exploitation tension into the problem.

Model-free reinforcement learning (RL) algorithms, such as Q-learning, directly parameterize and update value functions or policies without explicitly modeling the environment. They are typically simpler, more flexible to use, and thus more prevalent in modern deep RL than model-based approaches. However, empirical work has suggested that model-free algorithms may require more samples to learn [7, 22]. The theoretical question of "whether model-free algorithms can be made sample efficient" is one of the most fundamental questions in RL, and remains unsolved even in the basic scenario with finitely many states and actions.

In this paper, we study private sparsification of graphs. In particular, we give an algorithm that given an input graph, returns a sparse graph which approximates the spectrum of the input graph while ensuring differential privacy. This allows one to solve many graph problems privately yet efficiently and accurately. This is exemplified with application of the proposed meta-algorithm to graph algorithms for privately answering cut-queries, as well as practical algorithms for computing MAX-CUT and SPARSEST-CUT with better accuracy than previously known. We also give an efficient private algorithm to learn Laplacian eigenmap on a graph.

In this paper, we develop the first one-pass streaming algorithm for submodular maximization that does not evaluate the entire stream even once. By carefully subsampling each element of the data stream, our algorithm enjoys the tightest approximation guarantees in various settings while having the smallest memory footprint and requiring the lowest number of function evaluations. More specifically, for a monotone submodular function and a p-matchoid constraint, our randomized algorithm achieves a 4p approximation ratio (in expectation) with O(k) memory and O(km/p) queries per element (k is the size of the largest feasible solution and m is the number of matroids used to define the constraint).

While conventional methods require per-scene optimization, more recently several feed-forward methods have been proposed to generate pixel-aligned Gaussian representations with a learnable network, which are generalizable to different scenes. However, these methods simply combine pixel-aligned Gaussians from multiple views as scene representations, thereby leading to artifacts and extra memory cost without fully capturing the relations of Gaussians from different images. In this paper, we propose Gaussian Graph Network (GGN) to generate efficient and generalizable Gaussian representations. Specifically, we construct Gaussian Graphs to model the relations of Gaussian groups from different views. To support message passing at Gaussian level, we reformulate the basic graph operations over Gaussian representations, enabling each Gaussian to benefit from its connected Gaussian groups with Gaussian feature fusion.

Today's online platforms heavily lean on algorithmic recommendations for bolstering user engagement and driving revenue. However, these recommendations can impact multiple stakeholders simultaneously--the platform, items (sellers), and users (customers)--each with their unique objectives, making it difficult to find the right middle ground that accommodates all stakeholders.