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Existing performance measures for bandit algorithms such as regret, PAC bounds, or uniform-PAC (Dann et al., 2017), typically evaluate the cumulative performance, while allowing the play of an arbitrarily bad arm at any finite time t. Such a behavior can be highly detrimental in high-stakes applications. This paper introduces a stronger performance measure, the uniform last-iterate (ULI) guarantee, capturing both cumulative and instantaneous performance of bandit algorithms. Specifically, ULI characterizes the instantaneous performance since it ensures that the per-round regret of the played arm is bounded by a function, monotonically decreasing w.r.t. (large) round t, preventing revisits to bad arms when sufficient samples are available. We demonstrate that a near-optimal ULI guarantee directly implies near-optimal cumulative performance across aforementioned performance measures. To examine the achievability of ULI in the finite arm setting, we first provide two positive results that some elimination-based algorithms and high-probability adversarial algorithms with stronger analysis or additional designs, can attain near-optimal ULI guarantees. Then, we also provide a negative result, indicating that optimistic algorithms cannot achieve a near-optimal ULI guarantee. Finally, we propose an efficient algorithm for linear bandits with infinitely many arms, which achieves the ULI guarantee, given access to an optimization oracle.

Existing online learning algorithms for adversarial Markov Decision Processes achieve ${O}(\sqrt{T})$ regret after $T$ rounds of interactions even if the loss functions are chosen arbitrarily by an adversary, with the caveat that the transition function has to be fixed. This is because it has been shown that adversarial transition functions make no-regret learning impossible. Despite such impossibility results, in this work, we develop algorithms that can handle both adversarial losses and adversarial transitions, with regret increasing smoothly in the degree of maliciousness of the adversary. More concretely, we first propose an algorithm that enjoys $\widetilde{{O}}(\sqrt{T} + C^{\textsf{P}})$ regret where $C^{\textsf{P}}$ measures how adversarial the transition functions are and can be at most ${O}(T)$. While this algorithm itself requires knowledge of $C^{\textsf{P}}$, we further develop a black-box reduction approach that removes this requirement. Moreover, we also show that further refinements of the algorithm not only maintains the same regret bound, but also simultaneously adapts to easier environments (where losses are generated in a certain stochastically constrained manner as in Jin et al. [2021]) and achieves $\widetilde{{O}}(U + \sqrt{UC^{\textsf{L}}} + C^{\textsf{P}})$ regret, where $U$ is some standard gap-dependent coefficient and $C^{\textsf{L}}$ is the amount of corruption on losses., Comment: Update the camera-ready version for NeurIPS 2023

Tianwen-1 spacecraft (Wan et al. 2020) is China's first Mars exploration mission. The Mars Orbiter Magnetometer (MOMAG) is a scientific instrument aboard the Tianwen-1 mission that is designed to study magnetic fields at Mars, including the solar wind to the magnetosheath and the ionosphere. Using the first Tianwen-1/MOMAG data that is publicly available, we present interplanetary coronal mass ejection (ICME) and stream interaction region (SIR) catalogues based on in-situ observations at Mars between November 16, 2021, and December 31, 2021. We compared the magnetic field intensity and vector magnetic field measurements from Tianwen-1/MOMAG and Mars Atmospheric Volatile EvolutioN (MAVEN)/MAG during the ICME and SIR interval and found a generally good consistency between them. Due to MAVEN's orbital adjustment since 2019, the Tianwen-1/MOMAG instrument is currently the almost unique interplanetary magnetic field monitor at Mars. The observations indicate that the MOMAG instrument on Tianwen-1 is performing well and can provide accurate measurements of the vector magnetic field in the near-Mars solar wind space. The multi-point observations combining MOMAG, MINPA, and MEPA on board Tianwen-1 with MAG, SWIA, and STATIC on board MAVEN will open a window to systematically study the characteristic of ICMEs and SIRs at Mars, and their influences on the Martian atmosphere and ionosphere.

We study the problem of designing adaptive multi-armed bandit algorithms that perform optimally in both the stochastic setting and the adversarial setting simultaneously (often known as a best-of-both-world guarantee). A line of recent works shows that when configured and analyzed properly, the Follow-the-Regularized-Leader (FTRL) algorithm, originally designed for the adversarial setting, can in fact optimally adapt to the stochastic setting as well. Such results, however, critically rely on an assumption that there exists one unique optimal arm. Recently, Ito (2021) took the first step to remove such an undesirable uniqueness assumption for one particular FTRL algorithm with the $\frac{1}{2}$-Tsallis entropy regularizer. In this work, we significantly improve and generalize this result, showing that uniqueness is unnecessary for FTRL with a broad family of regularizers and a new learning rate schedule. For some regularizers, our regret bounds also improve upon prior results even when uniqueness holds. We further provide an application of our results to the decoupled exploration and exploitation problem, demonstrating that our techniques are broadly applicable., Comment: Update the camera-ready version for NeurIPS 2023