We list all notations used in this paper in Table 1.

Motivated by the scenario of large-scale learning in distributed systems, this paper studies a scenario where M agents cooperate together to solve the same instance of a K-armed stochastic bandit problem. The agents have limited access to a local subset of arms and are asynchronous with different gaps between decision-making rounds. The goal is to find the global optimal arm, and agents are able to pull any arm; however, they can only observe the reward when the selected arm is local. The challenge is a tradeoff for agents between pulling a local arm with observable feedback or pulling external arms without feedback and relying on others' observations that occur at different rates. We propose AAE-LCB, a two-stage algorithm that prioritizes pulling local arms following an active arm elimination policy and switches to other arms only if all local arms are dominated by some external arms. We analyze the regret of AAE-LCBand show it matches the regret lower bound up to a small factor.

Denoising Diffusion Probabilistic Models (DDPMs) provide the foundation for the recent breakthroughs in generative modeling. Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete. In this paper, we introduce Star-Shaped DDPM (SS-DDPM). Its star-shaped diffusion process allows us to bypass the need to define the transition probabilities or compute posteriors. We establish duality between star-shaped and specific Markovian diffusions for the exponential family of distributions and derive efficient algorithms for training and sampling from SS-DDPMs. In the case of Gaussian distributions, SS-DDPM is equivalent to DDPM. However, SS-DDPMs provide a simple recipe for designing diffusion models with distributions such as Beta, von Mises-Fisher, Dirichlet, Wishart and others, which can be especially useful when data lies on a constrained manifold. We evaluate the model in different settings and find it competitive even on image data, where Beta SS-DDPM achieves results comparable to a Gaussian DDPM.

This section provides more details about Shapley values in Section 3 of the paper. Linearity: If two independent games vand wcan be merged into one game u(S) = v(S)+w(S), then the Shapley value of the player i in game v and game w also can be merged, i.e. φu(i) = φv(i)+φw(i). Nullity: A dummy player isatisfies S N\{i},v(S {i}) = v(S)+v({i}), which indicates that the player ihas no interaction with other players, i.e. φ(i) = v({i}). Efficiency: The overall reward can be allocated to all players in the game, i.e. This section provides more details about multi-order interactions [8] in Section 3.3 of the paper.

In this paper, we evaluate the quality of knowledge representations encoded in deep neural networks (DNNs) for 3D point cloud processing. We propose a method to disentangle the overall model vulnerability into the sensitivity to the rotation, the translation, the scale, and local 3D structures. Besides, we also propose metrics to evaluate the spatial smoothness of encoding 3D structures, and the representation complexity of the DNN. Based on such analysis, experiments expose representation problems with classic DNNs, and explain the utility of the adversarial training. The code will be released when this paper is accepted.

In two-player zero-sum extensive-form games, Nash equilibrium prescribes optimal strategies against perfectly rational opponents. However, it does not guarantee rational play in parts of the game tree that can only be reached by the players making mistakes. This can be problematic when operationalizing equilibria in the real world among imperfect players. Trembling-hand refinements are a sound remedy to this issue, and are subsets of Nash equilibria that are designed to handle the possibility that any of the players may make mistakes. In this paper, we initiate the study of equilibrium refinements for settings where one of the players is perfectly rational (the "machine") and the other may make mistakes.

In two-player zero-sum extensive-form games, Nash equilibrium prescribes optimal strategies against perfectly rational opponents. However, it does not guarantee rational play in parts of the game tree that can only be reached by the players making mistakes. This can be problematic when operationalizing equilibria in the real world among imperfect players. Trembling-hand refinements are a sound remedy to this issue, and are subsets of Nash equilibria that are designed to handle the possibility that any of the players may make mistakes. In this paper, we initiate the study of equilibrium refinements for settings where one of the players is perfectly rational (the "machine") and the other may make mistakes.