arXiv subjects

Kavya Ravichandran

Publications and source records attributed to Kavya Ravichandran.

8 recordsLinked to original sources

arXiv2026

Algorithmic Approaches to Sequential Decision-Making and Social Epistemology

As humans, we face many decisions that require us to choose between sticking to something and giving up. This thesis uses algorithmic tools to derive insights about such decision-making problems in theoretical models, studying both near-optimal methods and outcomes of social and behavioral influences. Along the way, this thesis sheds light on what we gain and what we lose as we move from a messy and complex real world setting to a very general abstract model by studying various points along this spectrum. In Part I, we study algorithms for sequential decision-making in the improving multi-armed bandits problem. We provide nearly matching upper and lower bounds in the general case. Then, we then ask what is possible if we have access to similar instances to the one we wish to deploy our algorithm on. To that end, we provide guarantees in the data-driven algorithm design framework, showing that a polynomial number of samples is sufficient for learning good algorithms from a class of algorithms. In Part II, we study algorithmic approaches for problems in social epistemology. We start by analyzing what role theoretical models can play in the study of social problems. We then study social and behavioral influences in decision-making requiring investment. First, we provide mathematical formalism in which to study the formation of pessimism traps, a phenomenon identified by philosophers in which agents are influenced by their predecessors to engage in less-ambitious goals. We develop financial interventions to sustainably shift communities out of these traps. The second problem we study is the influence of grit as a behavioral trait in ambitious decision-making. Overall, these works seek to theoretically model phenomena in social epistemology and provide a framework for intervening algorithmically.

cs.DS↗

arXiv2025

Algorithm Design and Stronger Guarantees for the Improving Multi-Armed Bandits Problem

The improving multi-armed bandits problem is a formal model for allocating effort under uncertainty, motivated by scenarios such as investing research effort into new technologies, performing clinical trials, and hyperparameter selection from learning curves. Each pull of an arm provides reward that increases monotonically with diminishing returns. A growing line of work has designed algorithms for improving bandits, albeit with somewhat pessimistic worst-case guarantees. Indeed, strong lower bounds of $\Omega(k)$ and $\Omega(\sqrt{k})$ multiplicative approximation factors are known for both deterministic and randomized algorithms (respectively) relative to the optimal arm, where $k$ is the number of bandit arms. In this work, we propose two new parameterized families of bandit algorithms and bound the sample complexity of learning the near-optimal algorithm from each family using offline data. We also perform empirical evaluations on standard hyperparameter tuning benchmarks. The first family we define includes the optimal randomized algorithm from prior work. We show that an appropriately chosen algorithm from this family can achieve stronger guarantees, with optimal dependence on $k$, when the arm reward curves satisfy additional properties related to the strength of concavity. Our second family contains algorithms that both guarantee best-arm identification on well-behaved instances and revert to worst-case guarantees on poorly-behaved instances.

cs.LG↗

arXiv2025

A Theoretical Model for Grit in Pursuing Ambitious Ends

Ambition and risk-taking have been heralded as important ways for marginalized communities to get out of cycles of poverty. As a result, educational messaging often encourages individuals to strengthen their personal resolve and develop characteristics such as discipline and grit to succeed in ambitious ends. However, recent work in philosophy and sociology highlights that this messaging often does more harm than good for students in these situations. We study similar questions using a different epistemic approach and in simple theoretical models -- we provide a quantitative model of decision-making between stable and risky choices in the improving multi-armed bandits framework. We use this model to first study how individuals' "strategies" are affected by their level of grittiness and how this affects their accrued rewards. Then, we study the impact of various interventions, such as increasing grit or providing a financial safety net. Our investigation of rational decision making involves two different formal models of rationality, the competitive ratio between the accrued reward and the optimal reward and Bayesian quantification of uncertainty.

cs.CY↗

arXiv2025

Pessimism Traps and Algorithmic Interventions

In this paper, we relate the philosophical literature on pessimism traps to information cascades, a formal model derived from the economics and mathematics literature. A pessimism trap is a social pattern in which individuals in a community, in situations of uncertainty, begin to copy the sub-optimal actions of others, despite their individual beliefs. This maps nicely onto the concept of an information cascade, which involves a sequence of agents making a decision between two alternatives, with a private signal of the superior alternative and a public history of others' actions. Key results from the economics literature show that information cascades occur with probability one in many contexts, and depending on the strength of the signal, populations can fall into the incorrect cascade very easily and quickly. Once formed, in the absence of external perturbation, a cascade cannot be broken -- therefore, we derive an intervention that can be used to nudge a population from an incorrect to a correct cascade and, importantly, maintain the cascade once the subsidy is discontinued. We study this both theoretically and empirically.

cs.SI↗

arXiv2024

A Model for Combinatorial Dictionary Learning and Inference

We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a combinatorial model in which to study this question, motivated by the way objects occlude each other in a scene to form an image. First, we identify a property we call "well-structuredness" of a set of low-dimensional components which ensures that no two components in the set are too similar. We show how well-structuredness is sufficient for learning the set of latent components comprising a set of sample instances. We then consider the problem: given a set of components and an instance generated from some unknown subset of them, identify which parts of the instance arise from which components. We consider two variants: (1) determine the minimal number of components required to explain the instance; (2) determine the correct explanation for as many locations as possible. For the latter goal, we also devise a version that is robust to adversarial corruptions, with just a slightly stronger assumption on the components. Finally, we show that the learning problem is computationally infeasible in the absence of any assumptions.

cs.LG↗

arXiv2024

Nearly-tight Approximation Guarantees for the Improving Multi-Armed Bandits Problem

We give nearly-tight upper and lower bounds for the improving multi-armed bandits problem. An instance of this problem has $k$ arms, each of whose reward function is a concave and increasing function of the number of times that arm has been pulled so far. We show that for any randomized online algorithm, there exists an instance on which it must suffer at least an $Ω(\sqrt{k})$ approximation factor relative to the optimal reward. We then provide a randomized online algorithm that guarantees an $O(\sqrt{k})$ approximation factor, if it is told the maximum reward achievable by the optimal arm in advance. We then show how to remove this assumption at the cost of an extra $O(\log k)$ approximation factor, achieving an overall $O(\sqrt{k} \log k)$ approximation relative to optimal.

cs.LG↗

arXiv2024

Applying statistical learning theory to deep learning

Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how different architectures may lead to inductive bias when trained using gradient based methods. The goal of these lectures is to provide an overview of some of the main questions that arise when attempting to understand deep learning from a learning theory perspective. After a brief reminder on statistical learning theory and stochastic optimization, we discuss implicit bias in the context of benign overfitting. We then move to a general description of the mirror descent algorithm, showing how we may go back and forth between a parameter space and the corresponding function space for a given learning problem, as well as how the geometry of the learning problem may be represented by a metric tensor. Building on this framework, we provide a detailed study of the implicit bias of gradient descent on linear diagonal networks for various regression tasks, showing how the loss function, scale of parameters at initialization and depth of the network may lead to various forms of implicit bias, in particular transitioning between kernel or feature learning.

cs.LG↗

arXiv2022

Testing Tail Weight of a Distribution Via Hazard Rate

Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property testing, characterizing the number of samples required to to distinguish whether a distribution has a certain property or is far from having that property. In particular, given samples from a distribution, we seek to characterize the tail of the distribution, that is, understand how many elements appear infrequently. We develop an algorithm based on a careful bucketing scheme that distinguishes light-tailed distributions from non-light-tailed ones with respect to a definition based on the hazard rate, under natural smoothness and ordering assumptions. We bound the number of samples required for this test to succeed with high probability in terms of the parameters of the problem, showing that it is polynomial in these parameters. Further, we prove a hardness result that implies that this problem cannot be solved without any assumptions.

cs.LG↗