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Keerthana Gurushankar

Publications and source records attributed to Keerthana Gurushankar.

7 recordsLinked to original sources
arXiv2026

LookAhead: The Optimal Non-decreasing Index Policy for a Time-Varying Holding Cost problem

In practice, the cost of delaying a job can grow as the job waits. Such behavior is modeled by the Time-Varying Holding Cost (TVHC) problem, where each job's instantaneous holding cost increases with its current age (a job's age is the time since it arrived). The goal of the TVHC problem is to find a scheduling policy that minimizes the time-average total holding cost across all jobs. However, no optimality results are known for the TVHC problem outside of the asymptotic regime. In this paper, we study a simple yet still challenging special case: A two-class M/M/1 queue in which class 1 jobs incur a non-decreasing, time-varying holding cost and class 2 jobs incur a constant holding cost. Our main contribution is deriving the first optimal (non-decreasing) index policy for this special case of the TVHC problem. Our optimal policy, called LookAhead, stems from the following idea: Rather than considering each job's current holding cost when making scheduling decisions, we should look at their cost some $X$ time into the future, where this $X$ is intuitively called the ``lookahead amount." This paper derives that optimal lookahead amount.

cs.PF↗
arXiv2025

Improving Upon the generalized c-mu rule: a Whittle approach

Scheduling a stream of jobs whose holding cost changes over time is a classic and practical problem. Specifically, each job is associated with a holding cost (penalty), where a job's instantaneous holding cost is some increasing function of its class and current age (the time it has spent in the system since its arrival). The goal is to schedule the jobs to minimize the time-average total holding cost across all jobs. The seminal paper on this problem, by Van Mieghem in 1995, introduced the generalized c-mu rule for scheduling jobs. Since then, this problem has attracted significant interest but remains challenging due to the absence of a finite-dimensional state space formulation. Consequently, subsequent works focus on more tractable versions of this problem. This paper returns to the original problem, deriving a heuristic that empirically improves upon the generalized c-mu rule and all existing heuristics. Our approach is to first translate the holding cost minimization problem to a novel Restless Multi-Armed Bandit (R-MAB) problem with a finite number of arms. Based on our R-MAB, we derive a novel Whittle Index policy, which is both elegant and intuitive.

cs.PF↗
arXiv2025

Latency Guarantees for Caching with Delayed Hits

In the classical caching problem, when a requested page is not present in the cache (i.e., a "miss"), it is assumed to travel from the backing store into the cache "before" the next request arrives. However, in many real-life applications, such as content delivery networks, this assumption is unrealistic. The "delayed-hits" model for caching, introduced by Atre, Sherry, Wang, and Berger, accounts for the latency between a missed cache request and the corresponding arrival from the backing store. This theoretical model has two parameters: the "delay" $Z$, representing the ratio between the retrieval delay and the inter-request delay in an application, and the "cache size" $k$, as in classical caching. Classical caching corresponds to $Z=1$, whereas larger values of $Z$ model applications where retrieving missed requests is expensive. Despite the practical relevance of the delayed-hits model, its theoretical underpinnings are still poorly understood. We present the first tight theoretical guarantee for optimizing delayed-hits caching: The "Least Recently Used" algorithm, a natural, deterministic, online algorithm widely used in practice, is $O(Zk)$-competitive, meaning it incurs at most $O(Zk)$ times more latency than the (offline) optimal schedule. Our result extends to any so-called "marking" algorithm.

cs.DS↗
arXiv2023

Capturing and Interpreting Unique Information

Partial information decompositions (PIDs), which quantify information interactions between three or more variables in terms of uniqueness, redundancy and synergy, are gaining traction in many application domains. However, our understanding of the operational interpretations of PIDs is still incomplete for many popular PID definitions. In this paper, we discuss the operational interpretations of unique information through the lens of two well-known PID definitions. We reexamine an interpretation from statistical decision theory showing how unique information upper bounds the risk in a decision problem. We then explore a new connection between the two PIDs, which allows us to develop an informal but appealing interpretation, and generalize the PID definitions using a common Lagrangian formulation. Finally, we provide a new PID definition that is able to capture the information that is unique. We also show that it has a straightforward interpretation and examine its properties.

cs.IT↗
arXiv2022

Extracting Unique Information Through Markov Relations

We propose two new measures for extracting the unique information in $X$ and not $Y$ about a message $M$, when $X, Y$ and $M$ are joint random variables with a given joint distribution. We take a Markov based approach, motivated by questions in fair machine learning, and inspired by similar Markov-based optimization problems that have been used in the Information Bottleneck and Common Information frameworks. We obtain a complete characterization of our definitions in the Gaussian case (namely, when $X, Y$ and $M$ are jointly Gaussian), under the assumption of Gaussian optimality. We also examine the consistency of our definitions with the partial information decomposition (PID) framework, and show that these Markov based definitions achieve non-negativity, but not symmetry, within the PID framework.

cs.IT↗
arXiv2021

A Minimal Intervention Definition of Reverse Engineering a Neural Circuit

In neuroscience, researchers have developed informal notions of what it means to reverse engineer a system, e.g., being able to model or simulate a system in some sense. A recent influential paper of Jonas and Kording, that examines a microprocessor using techniques from neuroscience, suggests that common techniques to understand neural systems are inadequate. Part of the difficulty, as a previous work of Lazebnik noted, lies in lack of formal language. We provide a theoretical framework for defining reverse engineering of computational systems, motivated by the neuroscience context. Of specific interest are recent works where, increasingly, interventions are being made to alter the function of the neural circuitry to both understand the system and treat disorders. Starting from Lazebnik's viewpoint that understanding a system means you can ``fix it'', and motivated by use-cases in neuroscience, we propose the following requirement on reverse engineering: once an agent claims to have reverse-engineered a neural circuit, they subsequently need to be able to: (a) provide a minimal set of interventions to change the input/output (I/O) behavior of the circuit to a desired behavior; (b) arrive at this minimal set of interventions while operating under bounded rationality constraints (e.g., limited memory) to rule out brute-force approaches. Under certain assumptions, we show that this reverse engineering goal falls within the class of undecidable problems. Next, we examine some canonical computational systems and reverse engineering goals (as specified by desired I/O behaviors) where reverse engineering can indeed be performed. Finally, using an exemplar network, the ``reward network'' in the brain, we summarize the state of current neuroscientific understanding, and discuss how computer-science and information-theoretic concepts can inform goals of future neuroscience studies.

cs.IT↗