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

Solutions to a system of Yang-Baxter matrix equations

In this article, we take a system, $XAX=BXB$, $XBX=AXA$, of Yang-Baxter type matrix equations that ``generalizes" the matrix Yang-Baxter equation. We completely characterize the case when $A,B$ are orthogonal idempotents

5G CORE REDUNDANCY FROM EVOLVED PACKET CORE

Presented herein is a technique to provide Fifth Generation (5G) core (5GC) redundancy from a Fourth Generation (4G) Evolved Packet Core (EPC). In particular, for a 4G-5G interworking scenario, if a Session Management Function (SMF) set is implemented, the technique presented herein provides that an initial combined SMF and control plane Packet Data Network (PDN) Gateway (PGW-C) [referred to herein as SMF+PGW-C] can provide to a Serving Gateway (SGW), at session creation time, address information of all the SMF+PGW-Cs belonging to the same SMF set. The SGW can use the address information to facilitate failover to an alternate SMF+PGW-C belonging to the SMF set, in case the initial SMF+PGW-C does not respond to the SGW

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 $C$

Contemporary environmental issues of landfill leachate: assessment & remedies

AbstractLandfills are the primary option for waste disposal all over the world. Most of the landfill sites across the world are old and are not engineered to prevent contamination of the underlying soil and groundwater by the toxic leachate. The pollutants from landfill leachate have accumulative and detrimental effect on the ecology and food chains leading to carcinogenic effects, acute toxicity and genotoxicity among human beings. Management of this highly toxic leachate presents a challenging problem to the regulatory authorities who have set specific regulations regarding maximum limits of contaminants in treated leachate prior to disposal into the environment to ensure minimal environmental impact. There are different stages of leachate management such as monitoring of its formation and flow into the environment, identification of hazards associated with it and its treatment prior to disposal into the environment. This review focuses on: (i) leachate composition, (ii) Plume migration, (iii) Contaminant fate, (iv) Leachate plume monitoring techniques, (v) Risk assessment techniques, Hazard rating methods, mathematical modeling, and (vi) Recent innovations in leachate treatment technologies. However, due to seasonal fluctuations in leachate composition, flow rate and leachate volume, the management approaches cannot be stereotyped. Every scenario is unique and the strategy will vary accordingly. This paper lays out the choices for making an educated guess leading to the best management option

Alteration of Endothelins: A Common Pathogenetic Mechanism in Chronic Diabetic Complications

Endothelin (ET) peptides perform several physiological, vascular, and nonvascular functions and are widely distributed in a number of tissues. They are altered in several disease processes including diabetes. Alteration of ETs have been demonstrated in organs of chronic diabetic complications in both experimental and clinical studies. The majority of the effects of ET alteration in diabetes are due to altered vascular function. Furthermore, ET antagonists have been shown to prevent structural and functional changes induced by diabetes in animal models. This review discusses the contribution of ETs in the pathogenesis and the potential role of ET antagonism in the treatment of chronic diabetic complications