Best Arm Identification in Stochastic Bandits: Beyond β−\beta-optimality

This paper investigates a hitherto unaddressed aspect of best arm identification (BAI) in stochastic multi-armed bandits in the fixed-confidence setting. Two key metrics for assessing bandit algorithms are computational efficiency and performance optimality (e.g., in sample complexity). In stochastic BAI literature, there have been advances in designing algorithms to achieve optimal performance, but they are generally computationally expensive to implement (e.g., optimization-based methods). There also exist approaches with high computational efficiency, but they have provable gaps to the optimal performance (e.g., the $\beta$-optimal approaches in top-two methods). This paper introduces a framework and an algorithm for BAI that achieves optimal performance with a computationally efficient set of decision rules. The central process that facilitates this is a routine for sequentially estimating the optimal allocations up to sufficient fidelity. Specifically, these estimates are accurate enough for identifying the best arm (hence, achieving optimality) but not overly accurate to an unnecessary extent that creates excessive computational complexity (hence, maintaining efficiency). Furthermore, the existing relevant literature focuses on the family of exponential distributions. This paper considers a more general setting of any arbitrary family of distributions parameterized by their mean values (under mild regularity conditions). The optimality is established analytically, and numerical evaluations are provided to assess the analytical guarantees and compare the performance with those of the existing ones

SPRT-based Efficient Best Arm Identification in Stochastic Bandits

This paper investigates the best arm identification (BAI) problem in stochastic multi-armed bandits in the fixed confidence setting. The general class of the exponential family of bandits is considered. The state-of-the-art algorithms for the exponential family of bandits face computational challenges. To mitigate these challenges, a novel framework is proposed, which views the BAI problem as sequential hypothesis testing, and is amenable to tractable analysis for the exponential family of bandits. Based on this framework, a BAI algorithm is designed that leverages the canonical sequential probability ratio tests. This algorithm has three features for both settings: (1) its sample complexity is asymptotically optimal, (2) it is guaranteed to be $\delta-$PAC, and (3) it addresses the computational challenge of the state-of-the-art approaches. Specifically, these approaches, which are focused only on the Gaussian setting, require Thompson sampling from the arm that is deemed the best and a challenger arm. This paper analytically shows that identifying the challenger is computationally expensive and that the proposed algorithm circumvents it. Finally, numerical experiments are provided to support the analysis

Time-Dependent Acoustic Waves Generated by Multiple Resonant Bubbles: Application to Acoustic Cavitation

We analyse the ultrasound waves reflected by multiple bubbles in the linearized time-dependent acoustic model. The generated time-dependent wave field is estimated close to the bubbles. The motivation of this study comes from the therapy modality using acoustic cavitation generated by injected bubbles into the region of interest. The goal is to create enough, but not too much, pressure in the region of interest to eradicate anomalies in that region. Here, we derive the dominant part of the generated acoustic field by a cluster of bubbles taking into account the (high) contrasts of their mass density and bulk as well as their general distribution in the given region. As consequences of these approximations, we highlight the following features: 1. If we use dimers (two close bubbles), or generally polymers, then we obtain a remarkable enhancement of the whole echo in the whole time. 2. If we distribute the bubbles every where in the region of interest,then we can derive the effective acoustic model which turns out to be a dispersive one. We show that, for a given desired pressure, we can tune the effective model to generate it

Acoustic Cavitation using Resonating Micro-Bubbles. Analysis in the Time-Domain

We study the time-domain acoustic wave propagation in the presence of a micro-bubble. This micro-bubble is characterized by a mass density and bulk modulus which are both very small as compared to the ones of the background vacuum. The goal is to estimate the amount of pressure that is created very near (at a distance proportional to the radius of the bubble) to the bubble. We show that, at that small distance, the dominating field is reminiscent to the wave created by a point-like obstacle modeled formally by a Dirac-like heterogeneity with support at the location of the bubble and the contrast between the bubble and background material as the scattering coefficient. As a conclusion, we can tune the bubbles material properties so that the pressure near it reaches a desired amount. Such design might be useful in the purpose of acoustic cavitation where one needs enough, but not too much, pressure to eliminate unwanted anomalies. The mathematical analysis is done using time-domain integral equations and asymptotic analysis techniques. A well known feature here is that the contrasting scales between the bubble and the background generate resonances (mainly the Minnaert one) in the time-harmonic regime. Such critical scales, and the generated resonances, are also reflected in the time-domain estimation of the acoustic wave. In particular, reaching the desired amount of pressure near the location of the bubble is possible only with such resonating bubbles

Robust Causal Bandits for Linear Models

Sequential design of experiments for optimizing a reward function in causal systems can be effectively modeled by the sequential design of interventions in causal bandits (CBs). In the existing literature on CBs, a critical assumption is that the causal models remain constant over time. However, this assumption does not necessarily hold in complex systems, which constantly undergo temporal model fluctuations. This paper addresses the robustness of CBs to such model fluctuations. The focus is on causal systems with linear structural equation models (SEMs). The SEMs and the time-varying pre- and post-interventional statistical models are all unknown. Cumulative regret is adopted as the design criteria, based on which the objective is to design a sequence of interventions that incur the smallest cumulative regret with respect to an oracle aware of the entire causal model and its fluctuations. First, it is established that the existing approaches fail to maintain regret sub-linearity with even a few instances of model deviation. Specifically, when the number of instances with model deviation is as few as $T^\frac{1}{2L}$, where $T$ is the time horizon and $L$ is the longest causal path in the graph, the existing algorithms will have linear regret in $T$. Next, a robust CB algorithm is designed, and its regret is analyzed, where upper and information-theoretic lower bounds on the regret are established. Specifically, in a graph with $N$ nodes and maximum degree $d$, under a general measure of model deviation $C$, the cumulative regret is upper bounded by $\tilde{\mathcal{O}}(d^{L-\frac{1}{2}}(\sqrt{NT} + NC))$ and lower bounded by $\Omega(d^{\frac{L}{2}-2}\max\{\sqrt{T},d^2C\})$. Comparing these bounds establishes that the proposed algorithm achieves nearly optimal $\tilde{\mathcal{O}}(\sqrt{T})$ regret when $C$ is $o(\sqrt{T})$ and maintains sub-linear regret for a broader range of $C$

Network analysis reveals common host protein/s modulating pathogenesis of neurotropic viruses

Network analysis through graph theory provides a quantitative approach to characterize specific proteins and their constituent assemblies that underlie host-pathogen interactions. In the present study, graph theory was used to analyze the interactome designed out of 50 differentially expressing proteins from proteomic analysis of Chandipura Virus (CHPV, Family: Rhabdoviridae) infected mouse brain tissue to identify the primary candidates for intervention. Using the measure of degree centrality, that quantifies the connectedness of a single protein within a milieu of several other interacting proteins, DJ-1 was selected for further molecular validation. To elucidate the generality of DJ-1’s role in propagating infection its role was also monitored in another RNA virus, Japanese Encephalitis Virus (JEV, Family: Flaviviridae) infection. Concurrently, DJ-1 got over-expressed in response to reactive oxygen species (ROS) generation following viral infection which in the early phase of infection migrated to mitochondria to remove dysfunctional mitochondria through the process of mitophagy. DJ-1 was also observed to modulate the viral replication and interferon responses along with low-density lipoprotein (LDL) receptor expression in neurons. Collectively these evidences reveal a comprehensive role for DJ-1 in neurotropic virus infection in the brain

Herbs Having Analgesic Activity

Healthcare maintains a high priority on pain management, and research to develop safer and more potent analgesics is ongoing. Natural goods, especially plants, have recently attracted renewed interest as potential sources of analgesic medications. In this study, various techniques are used to measure pain. The rich source of analgesics found in medicinal plants includes Moringa oleifera, Aloe barbadensis, Curcuma longa, Eugenia caryophyllata, Adhatoda vasica, Mentha piperita, Ocimum sanctum, Zingiber officinale, Lavandula angustifolia, Epilobium angustifolium, Dialium guineense, Sida acuta, Stylosanthes fruticose, Bougainvilla spectabilis, Ficus glomerata, Polyalithia longifolia, Calotropis gigantea, Tinospora cordifolia, Ageratina glabrata, Mangifera indica, Peperomia pellucida, Jatropha gossypifolia, Leonotis leonurus, Mimosa rubicaulis, Cussonia paniculate, Biebersteinia multifida, Alternanthera sessislis, Mentha arvensis, Oroxylum indicum, Tamarindus indica, Cucurbita maxima, Cucumis sativus, Emblica officinalis, Angiopteris evecta, Parastrephia lephidophylla, Peperomia pellucida, Scoparia dulcis, Ficus racemose, Eremostachys laciniata, Phlogacanthus thyrsiflorus, Kigelia pinnata, Molineria capitulate, Manihot esculenta, Ficus religiosa, Dalbergia sissoo, Grangea maderaspatana, Nothospondias staudtii, Rhodiola rosea, Juniperus communis, Erythrina variegate etc. The results reported in this review paper represent scientific knowledge that may be applied in the future to isolate potentially active molecules from some of these medicinal plants