Related papers: The Sample Complexity of Best-$k$ Items Selection …
This paper establishes the exact comparison complexity of finding an element repeated $n$ times in a $2n$-element array containing $n+1$ distinct values, under the equality-comparison model with $O(1)$ extra space. We present a simple…
We study the problem of contextual combinatorial semi-bandits, where input contexts are mapped into subsets of size $m$ of a collection of $K$ possible actions. In each round, the learner observes the realized reward of the predicted…
A fundamental challenge in interactive learning and decision making, ranging from bandit problems to reinforcement learning, is to provide sample-efficient, adaptive learning algorithms that achieve near-optimal regret. This question is…
Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an…
We study efficient PAC learning of homogeneous halfspaces in $\mathbb{R}^d$ in the presence of malicious noise of Valiant (1985). This is a challenging noise model and only until recently has near-optimal noise tolerance bound been…
Recently, Brand, Ganian and Simonov introduced a parameterized refinement of the classical PAC-learning sample complexity framework. A crucial outcome of their investigation is that for a very wide range of learning problems, there is a…
In this study, we derive Probably Approximately Correct (PAC) bounds on the asymptotic sample-complexity for RL within the infinite-horizon Markov Decision Process (MDP) setting that are sharper than those in existing literature. The…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
We consider the \emph{approximate minimum selection} problem in presence of \emph{independent random comparison faults}. This problem asks to select one of the smallest $k$ elements in a linearly-ordered collection of $n$ elements by only…
We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical…
In this paper, we address the top-$K$ ranking problem with a monotone adversary. We consider the scenario where a comparison graph is randomly generated and the adversary is allowed to add arbitrary edges. The statistician's goal is then to…
We consider two multi-armed bandit problems with $n$ arms: (i) given an $\epsilon > 0$, identify an arm with mean that is within $\epsilon$ of the largest mean and (ii) given a threshold $\mu_0$ and integer $k$, identify $k$ arms with means…
We consider the problem of determining the top-$k$ largest measurements from a dataset distributed among a network of $n$ agents with noisy communication links. We show that this scenario can be cast as a distributed convex optimization…
Efficient exploration is one of the key challenges for reinforcement learning (RL) algorithms. Most traditional sample efficiency bounds require strategic exploration. Recently many deep RL algorithms with simple heuristic exploration…
The pairwise objective paradigms are an important and essential aspect of machine learning. Examples of machine learning approaches that use pairwise objective functions include differential network in face recognition, metric learning,…
Many dynamic decision problems, such as robotic control, involve a series of tasks, many of which are unknown at training time. Typical approaches for these problems, such as multi-task and meta reinforcement learning, do not generalize…
Several recent works have proposed instance-dependent upper bounds on the number of episodes needed to identify, with probability $1-\delta$, an $\varepsilon$-optimal policy in finite-horizon tabular Markov Decision Processes (MDPs). These…
The widespread use and popularity of collaborative content sites (e.g., IMDB, Amazon, Yelp, etc.) has created rich resources for users to consult in order to make purchasing decisions on various products such as movies, e-commerce products,…
Reachability computations that rely on learned or estimated models require calibration in order to uphold confidence about their guarantees. Calibration generally involves sampling scenarios inside the reachable set. However, producing…
We study the problem of learning to partition users into groups, where one must learn the compatibilities between the users to achieve optimal groupings. We define four natural objectives that optimize for average and worst case…