20 accepted papers
Stochastic gradient descent (SGD) is a cornerstone algorithm for high-dimensional optimization, renowned for its empirical successes. Recent theoretical advances have provided a deep understanding of how SGD enables feature learning in high-dimensional nonlinear models, most notably the *single-inde…
Test-time scaling can improve model performance by aggregating stochastic reasoning trajectories. However, achieving sample-efficient test-time self-consistency under a limited budget remains an open challenge. We introduce PETS (\textbf{P}rincipled and \textbf{E}fficient \textbf{T}est-Time \textbf{…
We study the contextual pricing problem, where in each round a seller observes a context, sets a price, and receives a binary purchase signal. We adopt a semi-parametric model in which the demand follows a linear parametric form composed with an unknown link function from a $\beta$-Hölder class. Pri…
Existing auto-bidding algorithms in digital advertising often treat the value of an ad opportunity as the revenue obtained when an ad is shown and/or clicked, and bid accordingly. This can lead to wasteful spending because the true value is the marginal gain from paid exposure: even without winning …
We study the evolution of information in interactive decision making through the lens of a stochastic multi-armed bandit problem. Focusing on a fundamental example where a unique optimal arm outperforms the rest by a fixed margin, we characterize the optimal success probability and mutual informatio…
We develop a unifying framework for information-theoretic lower bound in statistical estimation and interactive decision making. Classical lower bound techniques---such as Fano's method, Le Cam's method, and Assouad's lemma---are central to the study of minimax risk in statistical estimation, yet ar…
The classical theory of statistical estimation aims to estimate a parameter of interest under data generated from a fixed design (''offline estimation''), while the contemporary theory of online learning provides algorithms for estimation under adaptively chosen covariates (''online estimation''). M…
We consider contextual bandits with graph feedback, a class of interactive learning problems with richer structures than vanilla contextual bandits, where taking an action reveals the rewards for all neighboring actions in the feedback graph under all contexts. Unlike the multi-armed bandits setting…
In a carbon auction, licenses for CO2 emissions are allocated among multiple interested players. Inspired by this setting, we consider repeated multi-unit auctions with uniform pricing, which are widely used in practice. Our contribution is to analyze these auctions in both the offline and online se…
In the infinite-armed bandit problem, each arm's average reward is sampled from an unknown distribution, and each arm can be sampled further to obtain noisy estimates of the average reward of that arm. Prior work focuses on the best arm, i.e. estimating the maximum of the average reward distribution…
With the advent and increasing consolidation of e-commerce, digital advertising has very recently replaced traditional advertising as the main marketing force in the economy. In the past four years, a particularly important development in the digital advertising industry is the shift from second-pri…
We study the design of computationally efficient online learning algorithms under smoothed analysis. In this setting, at every step, an adversary generates a sample from an adaptively chosen distribution whose density is upper bounded by $1/\sigma$ times the uniform density. Given access to an offli…
In this paper we study the adversarial combinatorial bandit with a known non-linear reward function, extending existing work on adversarial linear combinatorial bandit. {The adversarial combinatorial bandit with general non-linear reward is an important open problem in bandit literature, and it is s…
Recent years have witnessed the success of adaptive (or unified) approaches in estimating symmetric properties of discrete distributions, where the learner first obtains a distribution estimator independent of the target property, and then plugs the estimator into the target property as the final es…
We study the statistical guarantees for the Imitation Learning (IL) problem in episodic MDPs. Rajaraman et al. (2020) show an information theoretic lower bound that in the worst case, a learner which can even actively query the expert policy suffers from a suboptimality growing quadratically in the…
We study the following learning problem with dependent data: Given a trajectory of length $n$ from a stationary Markov chain with $k$ states, the goal is to predict the distribution of the next state. For $3 \leq k \leq O(\sqrt{n})$, the optimal prediction risk in the Kullback-Leibler divergence is…
A central goal of causal inference is to detect and estimate the treatment effects of a given treatment or intervention on an outcome variable of interest, where a member known as the heterogeneous treatment effect (HTE) is of growing popularity in recent practical applications such as the personali…
In this paper, we study the multi-armed bandit problem in the batched setting where the employed policy must split data into a small number of batches. While the minimax regret for the two-armed stochastic bandits has been completely characterized in \cite{perchet2016batched}, the effect of the numb…
Entropy estimation is one of the prototypical problems in distribution property testing. To consistently estimate the Shannon entropy of a distribution on $S$ elements with independent samples, the optimal sample complexity scales sublinearly with $S$ as $\Theta(\frac{S}{\log S})$ as shown by Valian…
We analyze the Kozachenko–Leonenko (KL) fixed k-nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance for any fixed k over H\"{o}lder balls on a torus without assuming any conditions on how close the density could be from zero. Accompanyi…