Best-of-Both-Worlds Algorithms for Partial Monitoring

This study considers the partial monitoring problem with $k$-actions and $d$-outcomes and provides the first best-of-both-worlds algorithms, whose regrets are favorably bounded both in the stochastic and adversarial regimes. In particular, we show that for non-degenerate locally observable games, the regret is $O(m^2 k^4 \log(T) \log(k_{\Pi} T) / \Delta_{\min})$ in the stochastic regime and $O(m k^{2/3} \sqrt{T \log(T) \log k_{\Pi}})$ in the adversarial regime, where $T$ is the number of rounds, $m$ is the maximum number of distinct observations per action, $\Delta_{\min}$ is the minimum suboptimality gap, and $k_{\Pi}$ is the number of Pareto optimal actions. Moreover, we show that for globally observable games, the regret is $O(c_{\mathcal{G}}^2 \log(T) \log(k_{\Pi} T) / \Delta_{\min}^2)$ in the stochastic regime and $O((c_{\mathcal{G}}^2 \log(T) \log(k_{\Pi} T))^{1/3} T^{2/3})$ in the adversarial regime, where $c_{\mathcal{G}}$ is a game-dependent constant. We also provide regret bounds for a stochastic regime with adversarial corruptions. Our algorithms are based on the follow-the-regularized-leader framework and are inspired by the approach of exploration by optimization and the adaptive learning rate in the field of online learning with feedback graphs.Comment: 31 page

Stability-penalty-adaptive Follow-the-regularized-leader: Sparsity, Game-dependency, and Best-of-both-worlds

Adaptivity to the difficulties of a problem is a key property in sequential decision-making problems to broaden the applicability of algorithms. Follow-the-Regularized-Leader (FTRL) has recently emerged as one of the most promising approaches for obtaining various types of adaptivity in bandit problems. Aiming to further generalize this adaptivity, we develop a generic adaptive learning rate, called Stability-Penalty-Adaptive (SPA) learning rate for FTRL. This learning rate yields a regret bound jointly depending on stability and penalty of the algorithm, into which the regret of FTRL is typically decomposed. With this result, we establish several algorithms with three types of adaptivity: sparsity, game-dependency, and Best-of-Both-Worlds (BOBW). Sparsity frequently appears in real-world problems. However, existing sparse multi-armed bandit algorithms with $k$-arms assume that the sparsity level $s \leq k$ is known in advance, which is often not the case in real-world scenarios. To address this problem, with the help of the new learning rate framework, we establish $s$-agnostic algorithms with regret bounds of $\tilde{O}(\sqrt{sT})$ in the adversarial regime for $T$ rounds, which matches the existing lower bound up to a logarithmic factor. Meanwhile, BOBW algorithms aim to achieve a near-optimal regret in both the stochastic and adversarial regimes. Leveraging the new adaptive learning rate framework and a novel analysis to bound the variation in FTRL output in response to changes in a regularizer, we establish the first BOBW algorithm with a sparsity-dependent bound. Additionally, we explore partial monitoring and demonstrate that the proposed learning rate framework allows us to achieve a game-dependent bound and the BOBW simultaneously.Comment: 30 page

Adaptive Learning Rate for Follow-the-Regularized-Leader: Competitive Analysis and Best-of-Both-Worlds

Follow-The-Regularized-Leader (FTRL) is known as an effective and versatile approach in online learning, where appropriate choice of the learning rate is crucial for smaller regret. To this end, we formulate the problem of adjusting FTRL's learning rate as a sequential decision-making problem and introduce the framework of competitive analysis. We establish a lower bound for the competitive ratio and propose update rules for learning rate that achieves an upper bound within a constant factor of this lower bound. Specifically, we illustrate that the optimal competitive ratio is characterized by the (approximate) monotonicity of components of the penalty term, showing that a constant competitive ratio is achievable if the components of the penalty term form a monotonically non-increasing sequence, and derive a tight competitive ratio when penalty terms are $\xi$-approximately monotone non-increasing. Our proposed update rule, referred to as \textit{stability-penalty matching}, also facilitates constructing the Best-Of-Both-Worlds (BOBW) algorithms for stochastic and adversarial environments. In these environments our result contributes to achieve tighter regret bound and broaden the applicability of algorithms for various settings such as multi-armed bandits, graph bandits, linear bandits, and contextual bandits

Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and localization in matrix models

We study reduced matrix models obtained by the dimensional reduction of N=2 quiver Chern-Simons theories on S^3 to zero dimension and show that if a reduced model is expanded around a particular multiple fuzzy sphere background, it becomes equivalent to the original theory on S^3 in the large-N limit. This is regarded as a novel large-N reduction on a curved space S^3. We perform the localization method to the reduced model and compute the free energy and the vacuum expectation value of a BPS Wilson loop operator. In the large-N limit, we find an exact agreement between these results and those in the original theory on S^3.Comment: 46 pages, 11 figures; minor modification

Improved scientific ballooning applied to the cryo-sampling experiment at Syowa Station

On January 3, 1998, a large balloon (30000 m^3) was successfully launched at Syowa Station for the cryo-sampling of the stratospheric atmosphere. The sampling system splashed down in the Liitzow-Holm Bay and recovered by icebreaker SHIRASE. The cryo-sampling at Antarctica was the first trial in the world and the recovery of a heavy payload was also the first challenge at Syowa Station. A lot of new ballooning technologies were applied to this operation, such as compact balloon launching equipments, a reliable recovery system, a handy ground radio station for the balloon tracking and data acquisition and so forth. The realtime flight data could be received at National Institute of Polar Research (NIPR) in Tokyo by using the computer network via INMARSAT. At NIPR the collaboration members could monitor the entire process of the experiment at Syowa Station in detail and send some instructions and advice. This balloon experiment showed an extended possibility of a large scale scientific ballooning at Syowa Station. This paper deals with those newly developed balloon engineering technologies

Studies on the Tolerance of Grape Vines to Potassium Chlortate. : (I). On the Differences of Tolerance to Potassium Chlolate among the Varieties(1).

1.葡萄の穂品種11種及び台品種4種について栽培実験することなく,それらの葉のKClO3抗毒性の大小によって耐乾性の強弱または少なくともILJINのいうDesciccation Resistanceの強弱を推定する目安を得る目的で本実験を行った.8月下旬から10月下旬にわたり,午後3時頃採葉したものを直ちに0.03%を標準とするKClO3液に挿し,24時間暗所に置いた後,清水に替えて明所に24～72時間置いて葉面に現われる害徴を判定した.2.穂品種の害徴度指数をみるとMuscat of Alexandriaは0,甲州,Neo Muscat及びMuscat Bailey Aは10～11,Campbell Early,巨峰,甲州3尺及びGros Colmanは17～20であった.DelawareはCampbell Earlyよりも抗毒性やや強く,Red MillenniumではMuscat Bailey Aより稍弱い.3.Berlandieri×Riparia 420AはCampbell Earlyよりも抗毒性弱く,Hybrid Francは甲州と同程度である.Riparia×Rupestris 3306は同3309より抗毒性がやや弱い.本実験の範囲内では葡萄の穂品種間ではそれらの耐乾性の強弱とKClO3抗毒性の大小と比例するが,台品種間では逆に比例するものゝ如くである.4.同じく東洋系欧州種に属するといわれる甲州と甲州3尺において後者は前者よりはるかに抗毒性が小であること,及びMuscat of Alexandria種と甲州3尺の交配種であるNeo Muscatの抗毒性が両者の中間であることなどは注目に値する.5.同一樹上の葉相互間にもKClO3抗毒性に個体差が認められる

Intercellular exchange of Wnt ligands reduces cell population heterogeneity during embryogenesis

Wnt signaling is required to maintain bipotent progenitors for neural and paraxial mesoderm cells, the neuromesodermal progenitor (NMP) cells that reside in the epiblast and tailbud. Since epiblast/tailbud cells receive Wnt ligands produced by one another, this exchange may average out the heterogeneity of Wnt signaling levels among these cells. Here, we examined this possibility by replacing endogenous Wnt3a with a receptor-fused form that activates signaling in producing cells, but not in neighboring cells. Mutant mouse embryos show a unique phenotype in which maintenance of many NMP cells is impaired, although some cells persist for long periods. The epiblast cell population of these embryos increases heterogeneity in Wnt signaling levels as embryogenesis progresses and are sensitive to retinoic acid, an endogenous antagonist of NMP maintenance. Thus, mutual intercellular exchange of Wnt ligands in the epiblast cell population reduces heterogeneity and achieves robustness to environmental stress

Establishment of Neurospora crassa as a model organism for fungal virology

The filamentous fungus Neurospora crassa is used as a model organism for genetics, developmental biology and molecular biology. Remarkably, it is not known to host or to be susceptible to infection with any viruses. Here, we identify diverse RNA viruses in N. crassa and other Neurospora species, and show that N. crassa supports the replication of these viruses as well as some viruses from other fungi. Several encapsidated double-stranded RNA viruses and capsid-less positive-sense single-stranded RNA viruses can be experimentally introduced into N. crassa protoplasts or spheroplasts. This allowed us to examine viral replication and RNAi-mediated antiviral responses in this organism. We show that viral infection upregulates the transcription of RNAi components, and that Dicer proteins (DCL-1, DCL-2) and an Argonaute (QDE-2) participate in suppression of viral replication. Our study thus establishes N. crassa as a model system for the study of host-virus interactions. The fungus Neurospora crassa is a model organism for the study of various biological processes, but it is not known to be infected by any viruses. Here, Honda et al. identify RNA viruses that infect N. crassa and examine viral replication and RNAi-mediated antiviral responses, thus establishing this fungus as a model for the study of host-virus interactions