arXiv subjects

George Vershinin

Publications and source records attributed to George Vershinin.

5 recordsLinked to original sources

arXiv2025

On Cost-Aware Designs for Sequential Hypothesis Testing

We introduce Cost-Aware (CA) Sequential Hypothesis Testing (CASHT), in which an active decision-maker selects sensing actions with differing, random costs to identify the true hypothesis under an average-error constraint $\delta$ while minimizing the expected total cost rather than the number of samples. For fixed costs, we prove that the optimal expected total cost scales as $\Theta(\log(1/\delta))$, and is achievable by Multihypothesis Sequential Probability Ratio Test-based procedures. We show that the CA design principle is to maximize the ratio of expected information gain to expected cost under the policy-induced action distribution. Guided by this principle, we adapt two classic policies to the CA setting and establish their asymptotic optimality. We then treat random costs under two revelation models: ex-post, where costs are disclosed only after a sample is obtained, and the cost-error tradeoff coincides with the fixed-cost case, and ex-ante, where costs accrue before acquisition, and the decision maker may cancel an action mid-operation. For the ex-ante model, we characterize when cancellation lowers the total cost and analyze several cost distributions in detail. Simulations confirm our findings that the CA variants consistently reduce total cost relative to their classical counterparts, and when action cancellation helps or hurts.

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arXiv2025

Active Sequential Hypothesis Testing with Non-Homogeneous Costs

We study the Non-Homogeneous Sequential Hypothesis Testing (NHSHT), where a single active Decision-Maker (DM) selects actions with heterogeneous positive costs to identify the true hypothesis under an average error constraint $δ$, while minimizing expected total cost paid. Under standard arguments, we show that the objective decomposes into the product of the mean number of samples and the mean per-action cost induced by the policy. This leads to a key design principle: one should optimize the ratio of expectations (expected information gain per expected cost) rather than the expectation of per-step information-per-cost ("bit-per-buck"), which can be suboptimal. We adapt the Chernoff scheme to NHSHT, preserving its classical $\log 1/δ$ scaling. In simulations, the adapted scheme reduces mean cost by up to 50\% relative to the classic Chernoff policy and by up to 90\% relative to the naive bit-per-buck heuristic.

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arXiv2025

Iterative Hypothesis Pruning and Distribution-based Early Labeling for Sequential Hypothesis Testing

We consider the framework of Sequential Hypothesis Testing (SHT), in which a decision maker (DM) selects actions that generate samples from known, action-dependent distributions, while the realized distribution is determined by an unknown true hypothesis. To identify this hypothesis, we adopt the elimination perspective and propose three deterministic, adaptive, multi-iteration algorithms with a common structure, termed $\Phi$, $\Phi$-$\Delta$, and $I$. In each iteration, the DM selects an action and repeatedly applies it to collect samples, after which hypotheses inconsistent with the observed data are eliminated. The algorithms differ in the criterion used to terminate each iteration: $\Phi$ continues until one hypothesis dominates all others; $\Phi$-$\Delta$ first clusters hypotheses whose per-action distributions are close in total variation and then proceeds in the spirit of $\Phi$; $I$ continues until one hypothesis can be safely discarded. We analyze our algorithms, establishing: (i) controlled error-rates, (ii) controlled sample complexity, (iii) asymptotic optimality, (iv) computational complexity, and (v) NP-hardness of the optimal action-sequence selection for minimal sample complexity.

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arXiv2025

Multi-Stage Active Sequential Hypothesis Testing with Clustered Hypotheses

We consider the problem where an active Decision-Maker (DM) is tasked to identify the true hypothesis using as few as possible observations while maintaining accuracy. The DM collects observations according to its determined actions and knows the distributions under each hypothesis. We propose a deterministic and adaptive multi-stage hypothesis-elimination strategy where the DM selects an action, applies it repeatedly, and discards hypotheses in light of its obtained observations. The DM selects actions based on maximal separation expressed by the distance between the parameter vectors of each distribution under each hypothesis. Close distributions can be clustered, simplifying the search and significantly reducing the number of required observations. Our algorithms achieve vanishing Average Bayes Risk (ABR) as the error probability approaches zero, i.e., the algorithm is asymptotically optimal. Furthermore, we show that the ABR is bounded when the number of hypotheses grows. Simulations are carried out to evaluate the algorithm's performance compared to another multi-stage hypothesis-elimination algorithm, where an improvement of several orders of magnitude in the mean number of observations required is observed.

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arXiv2023

Order-optimal Joint Transmission and Identification in Massive Multi-User MIMO via Group Testing

The number of wireless devices which are connected to a single Wireless Local Area Network continues to grow each year. As a result, the orchestration of so many devices becomes a daunting, resource--consuming task, especially when the resources available at the single access point are limited, and it is hard to anticipate which devices will request access at any given time. On the other hand, the number of antennas on both the devices and the access point grows as well, facilitating advanced joint scheduling and coding techniques. In this paper, we leverage the large number of antennas and suggest a massive multiple-user multiple-input-multiple-output (MU-MIMO) scheme using sparse coding based on Group Testing (GT) principles. The scheme allows for a small subset of devices to transmit simultaneously, without a preceding scheduling phase or coordination, thus reducing overhead and complexity. Specifically, we show that out of a population of $N$ devices, it is possible to jointly identify and decode $K$ devices, unknown in advance, simultaneously and without any scheduling. The scheme utilizes minimal knowledge of channel state, uses an efficient (in both run-time and space) decoding algorithm, and requires $O(K\log N\mathcal{M})$ antennas, where $\mathcal{M}$ is the number of messages per device. In fact, we prove that this scheme is order--optimal in the number of users and messages. This is done by deriving sufficient conditions for a vanishing error probability (a direct result), bounding the minimal number of antennas necessary for any such scheme (a converse result), and showing that these results are asymptotically tight.

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