David A. Castañón

Mohammad Merati, H. M. Sabbir Ahmad, Wenchao Li et al.

We study online task allocation for multi-robot, multi-queue systems with asymmetric stochastic arrivals and switching delays. We formulate the problem in discrete time: each location can host at most one robot per slot, servicing a task consumes one slot, switching between locations incurs a one-slot travel delay, and arrivals at locations are independent Bernoulli processes with heterogeneous rates. Building on our previous structural result that optimal policies are of exhaustive type, we formulate a discounted-cost Markov decision process and develop an exhaustive-assignment actor-critic policy architecture that enforces exhaustive service by construction and learns only the next-queue allocation for idle robots. Unlike the exhaustive-serve-longest (ESL) queue rule, whose optimality is known only under symmetry, the proposed policy adapts to asymmetry in arrival rates. Across different server-location ratios, loads, and asymmetric arrival profiles, the proposed policy consistently achieves lower discounted holding cost and smaller mean queue length than the ESL baseline, while remaining near-optimal on instances where an optimal benchmark is available. These results show that structure-aware actor-critic methods provide an effective approach for real-time multi-robot scheduling.

Mohammad Merati, David Castañón

This paper presents a novel approach for optimizing the scheduling and control of Pan-Tilt-Zoom (PTZ) cameras in dynamic surveillance environments. The proposed method integrates Kalman filters for motion prediction with a dynamic network flow model to enhance real-time video capture efficiency. By assigning Kalman filters to tracked objects, the system predicts future locations, enabling precise scheduling of camera tasks. This prediction-driven approach is formulated as a network flow optimization, ensuring scalability and adaptability to various surveillance scenarios. To further reduce redundant monitoring, we also incorporate group-tracking nodes, allowing multiple objects to be captured within a single camera focus when appropriate. In addition, a value-based system is introduced to prioritize camera actions, focusing on the timely capture of critical events. By adjusting the decay rates of these values over time, the system ensures prompt responses to tasks with imminent deadlines. Extensive simulations demonstrate that this approach improves coverage, reduces average wait times, and minimizes missed events compared to traditional master-slave camera systems. Overall, our method significantly enhances the efficiency, scalability, and effectiveness of surveillance systems, particularly in dynamic and crowded environments.

Ali Siahkamari, Xide Xia, Venkatesh Saligrama et al.

Bregman divergences generalize measures such as the squared Euclidean distance and the KL divergence, and arise throughout many areas of machine learning. In this paper, we focus on the problem of approximating an arbitrary Bregman divergence from supervision, and we provide a well-principled approach to analyzing such approximations. We develop a formulation and algorithm for learning arbitrary Bregman divergences based on approximating their underlying convex generating function via a piecewise linear function. We provide theoretical approximation bounds using our parameterization and show that the generalization error $O_p(m^{-1/2})$ for metric learning using our framework matches the known generalization error in the strictly less general Mahalanobis metric learning setting. We further demonstrate empirically that our method performs well in comparison to existing metric learning methods, particularly for clustering and ranking problems.

Safa C. Medin, John Murray-Bruce, David Castañón et al.

Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires a simple trial allocation gain quantity. Motivated by realizing this gain without an oracle, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements: up to 4.36 dB for the estimation of p and up to 1.80 dB for the estimation of log p.

Huanyu Ding, David Castanon

The problem of search by multiple agents to find and localize objects arises in many important applications. In this paper, we study a class of multi-agent search problems in which each agent can access only a subset of a discrete search space, with detection performance that depends only on the location. We show that this problem can be reformulated as a minimum cost network optimization problem, and develop a fast specialized algorithm for the solution. We prove that our algorithm is correct, and has worst case computation performance that is faster than general minimum cost flow algorithms. We also address the problem where detection performance depends on both location and agent, which is known to be NP-Hard. We reduce the problem to a submodular maximization problem over a matroid, and provide an approximate algorithm with guaranteed performance. We illustrate the performance of our algorithms with simulations of search problems and compare it with other min-cost flow algorithms.

Huanyu Ding, David A. Castañón

The problem of searching for an unknown object occurs in important applications ranging from security, medicine and defense. Sensors with the capability to process information rapidly require adaptive algorithms to control their search in response to noisy observations. In this paper, we discuss classes of dynamic, adaptive search problems, and formulate the resulting sensor control problems as stochastic control problems with imperfect information, based on previous work on noisy search problems. The structure of these problems, with objective functions related to information entropy, allows for a complete characterization of the optimal strategies and the optimal cost for the resulting finite-horizon stochastic control problems. We study the problem where an individual sensor is capable of searching over multiple sub-regions in a time, and provide a constructive algorithm for determining optimal policies in real time based on convex optimization. We also study the problem in which there are multiple sensors, each of which is only capable of detecting over one sub-region in a time, jointly searching for an object. Whereas this can be viewed as a special case of our multi-region results, we show that the computation of optimal policies can be decoupled into single-sensor individual scalar convex optimization problems, and provide simple symmetry conditions where the solutions can be determined analytically. We also consider the case where individual sensors can select the accuracy of their sensing modes with different costs, and derive optimal strategies for these problems in terms of the solutions of scalar convex optimization problems. We illustrate our results with experiments using multiple sensors searching for a single object.

Kirill Trapeznikov, Venkatesh Saligrama, David Castanon

In many classification systems, sensing modalities have different acquisition costs. It is often {\it unnecessary} to use every modality to classify a majority of examples. We study a multi-stage system in a prediction time cost reduction setting, where the full data is available for training, but for a test example, measurements in a new modality can be acquired at each stage for an additional cost. We seek decision rules to reduce the average measurement acquisition cost. We formulate an empirical risk minimization problem (ERM) for a multi-stage reject classifier, wherein the stage $k$ classifier either classifies a sample using only the measurements acquired so far or rejects it to the next stage where more attributes can be acquired for a cost. To solve the ERM problem, we show that the optimal reject classifier at each stage is a combination of two binary classifiers, one biased towards positive examples and the other biased towards negative examples. We use this parameterization to construct stage-by-stage global surrogate risk, develop an iterative algorithm in the boosting framework and present convergence and generalization results. We test our work on synthetic, medical and explosives detection datasets. Our results demonstrate that substantial cost reduction without a significant sacrifice in accuracy is achievable.