BZPEERPapers, people, evidence and research paths
Menu

Discover

SearchFind papers, people, topics, institutions and opportunities from one place.GraphSee how papers, authors, topics and evidence connect.

Research tools

HomeContinue from the papers, people and topics that matter now.CollectionsTurn saved papers into reading lists, evidence maps and shareable context.ResearchReconstruct the path that led you from search to paper to question.CollaborationMove from a paper, topic or expert request into a focused thread.PublishCreate full-text research articles with metadata, formulas and versions.

Network

ExpertsFind specialists whose work and reviews explain why they can help.CommunitiesJoin research groups organized around papers, topics and shared evidence.

Opportunities

ListingsBrowse roles, calls and collaborations connected to real research context.

Account

Log inReturn to your saved papers, graph views and active threads.Create accountStart saving papers, building a research trail and joining teams.
Log inCreate account

Source author record

Nishant A. Mehta

Nishant A. Mehta appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Machine LearningArtificial Intelligence

Catalog footprint

What is connected

8works
2topics
4close collaborators

Actions

Connect this record

Log in to claim
Open graphBrowse works

Research graph

See the researcher in context

Open full explorer

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

8 published item(s)

preprint2026arXiv

Calibeating for general proper losses: A Bregman divergence approach

This work introduces a general framework for calibeating based on regret minimization. As compared to Foster and Hart's seminal calibeating work which had specialized treatments of Brier score (squared loss) and log loss, we consider a large family of proper losses that includes $α$-Tsallis losses (for $α\in [1, 2]$) and Lipschitz losses. Our results for Tsallis losses also hold for an unscaled version of Tsallis loss that recovers log loss. Our analysis is oriented around the Bregman divergence view of a proper loss. Technically, our results for the family of Tsallis losses that we consider are U-calibration results, simultaneously obtaining logarithmic regret for all losses in this family while having a weaker dependence on the dimension compared to previous results. Of potential independent interest, we also show a new regret equality for the regret of Be The Regularized Leader. This regret equality holds for general proper losses and itself is based on two results related to online updating formulas for the generalized variance, the latter being a previously introduced generalization of variance based on Bregman divergences.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Adversarial Online Multi-Task Reinforcement Learning

We consider the adversarial online multi-task reinforcement learning setting, where in each of $K$ episodes the learner is given an unknown task taken from a finite set of $M$ unknown finite-horizon MDP models. The learner's objective is to minimize its regret with respect to the optimal policy for each task. We assume the MDPs in $\mathcal{M}$ are well-separated under a notion of $λ$-separability, and show that this notion generalizes many task-separability notions from previous works. We prove a minimax lower bound of $Ω(K\sqrt{DSAH})$ on the regret of any learning algorithm and an instance-specific lower bound of $Ω(\frac{K}{λ^2})$ in sample complexity for a class of uniformly-good cluster-then-learn algorithms. We use a novel construction called 2-JAO MDP for proving the instance-specific lower bound. The lower bounds are complemented with a polynomial time algorithm that obtains $\tilde{O}(\frac{K}{λ^2})$ sample complexity guarantee for the clustering phase and $\tilde{O}(\sqrt{MK})$ regret guarantee for the learning phase, indicating that the dependency on $K$ and $\frac{1}{λ^2}$ is tight.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A Farewell to Arms: Sequential Reward Maximization on a Budget with a Giving Up Option

We consider a sequential decision-making problem where an agent can take one action at a time and each action has a stochastic temporal extent, i.e., a new action cannot be taken until the previous one is finished. Upon completion, the chosen action yields a stochastic reward. The agent seeks to maximize its cumulative reward over a finite time budget, with the option of "giving up" on a current action -- hence forfeiting any reward -- in order to choose another action. We cast this problem as a variant of the stochastic multi-armed bandits problem with stochastic consumption of resource. For this problem, we first establish that the optimal arm is the one that maximizes the ratio of the expected reward of the arm to the expected waiting time before the agent sees the reward due to pulling that arm. Using a novel upper confidence bound on this ratio, we then introduce an upper confidence based-algorithm, WAIT-UCB, for which we establish logarithmic, problem-dependent regret bound which has an improved dependence on problem parameters compared to previous works. Simulations on various problem configurations comparing WAIT-UCB against the state-of-the-art algorithms are also presented.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Fast rates with high probability in exp-concave statistical learning

We present an algorithm for the statistical learning setting with a bounded exp-concave loss in $d$ dimensions that obtains excess risk $O(d \log(1/δ)/n)$ with probability at least $1 - δ$. The core technique is to boost the confidence of recent in-expectation $O(d/n)$ excess risk bounds for empirical risk minimization (ERM), without sacrificing the rate, by leveraging a Bernstein condition which holds due to exp-concavity. We also show that with probability $1 - δ$ the standard ERM method obtains excess risk $O(d (\log(n) + \log(1/δ))/n)$. We further show that a regret bound for any online learner in this setting translates to a high probability excess risk bound for the corresponding online-to-batch conversion of the online learner. Lastly, we present two high probability bounds for the exp-concave model selection aggregation problem that are quantile-adaptive in a certain sense. The first bound is a purely exponential weights type algorithm, obtains a nearly optimal rate, and has no explicit dependence on the Lipschitz continuity of the loss. The second bound requires Lipschitz continuity but obtains the optimal rate.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

From Stochastic Mixability to Fast Rates

Empirical risk minimization (ERM) is a fundamental learning rule for statistical learning problems where the data is generated according to some unknown distribution $\mathsf{P}$ and returns a hypothesis $f$ chosen from a fixed class $\mathcal{F}$ with small loss $\ell$. In the parametric setting, depending upon $(\ell, \mathcal{F},\mathsf{P})$ ERM can have slow $(1/\sqrt{n})$ or fast $(1/n)$ rates of convergence of the excess risk as a function of the sample size $n$. There exist several results that give sufficient conditions for fast rates in terms of joint properties of $\ell$, $\mathcal{F}$, and $\mathsf{P}$, such as the margin condition and the Bernstein condition. In the non-statistical prediction with expert advice setting, there is an analogous slow and fast rate phenomenon, and it is entirely characterized in terms of the mixability of the loss $\ell$ (there being no role there for $\mathcal{F}$ or $\mathsf{P}$). The notion of stochastic mixability builds a bridge between these two models of learning, reducing to classical mixability in a special case. The present paper presents a direct proof of fast rates for ERM in terms of stochastic mixability of $(\ell,\mathcal{F}, \mathsf{P})$, and in so doing provides new insight into the fast-rates phenomenon. The proof exploits an old result of Kemperman on the solution to the general moment problem. We also show a partial converse that suggests a characterization of fast rates for ERM in terms of stochastic mixability is possible.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Minimax Multi-Task Learning and a Generalized Loss-Compositional Paradigm for MTL

Since its inception, the modus operandi of multi-task learning (MTL) has been to minimize the task-wise mean of the empirical risks. We introduce a generalized loss-compositional paradigm for MTL that includes a spectrum of formulations as a subfamily. One endpoint of this spectrum is minimax MTL: a new MTL formulation that minimizes the maximum of the tasks' empirical risks. Via a certain relaxation of minimax MTL, we obtain a continuum of MTL formulations spanning minimax MTL and classical MTL. The full paradigm itself is loss-compositional, operating on the vector of empirical risks. It incorporates minimax MTL, its relaxations, and many new MTL formulations as special cases. We show theoretically that minimax MTL tends to avoid worst case outcomes on newly drawn test tasks in the learning to learn (LTL) test setting. The results of several MTL formulations on synthetic and real problems in the MTL and LTL test settings are encouraging.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

On the Sample Complexity of Predictive Sparse Coding

The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task. Predictive sparse coding algorithms recently have demonstrated impressive performance on a variety of supervised tasks, but their generalization properties have not been studied. We establish the first generalization error bounds for predictive sparse coding, covering two settings: 1) the overcomplete setting, where the number of features k exceeds the original dimensionality d; and 2) the high or infinite-dimensional setting, where only dimension-free bounds are useful. Both learning bounds intimately depend on stability properties of the learned sparse encoder, as measured on the training sample. Consequently, we first present a fundamental stability result for the LASSO, a result characterizing the stability of the sparse codes with respect to perturbations to the dictionary. In the overcomplete setting, we present an estimation error bound that decays as \tilde{O}(sqrt(d k/m)) with respect to d and k. In the high or infinite-dimensional setting, we show a dimension-free bound that is \tilde{O}(sqrt(k^2 s / m)) with respect to k and s, where s is an upper bound on the number of non-zeros in the sparse code for any training data point.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

Generative and Latent Mean Map Kernels

We introduce two kernels that extend the mean map, which embeds probability measures in Hilbert spaces. The generative mean map kernel (GMMK) is a smooth similarity measure between probabilistic models. The latent mean map kernel (LMMK) generalizes the non-iid formulation of Hilbert space embeddings of empirical distributions in order to incorporate latent variable models. When comparing certain classes of distributions, the GMMK exhibits beneficial regularization and generalization properties not shown for previous generative kernels. We present experiments comparing support vector machine performance using the GMMK and LMMK between hidden Markov models to the performance of other methods on discrete and continuous observation sequence data. The results suggest that, in many cases, the GMMK has generalization error competitive with or better than other methods.

0 citations0 reviewsNo code linkedOpen access