arXiv subjects

Nika Haghtalab

Publications and source records attributed to Nika Haghtalab.

At least 55 records · Page 3Linked to original sources

arXiv2023

Leveraging Reviews: Learning to Price with Buyer and Seller Uncertainty

In online marketplaces, customers have access to hundreds of reviews for a single product. Buyers often use reviews from other customers that share their type -- such as height for clothing, skin type for skincare products, and location for outdoor furniture -- to estimate their values, which they may not know a priori. Customers with few relevant reviews may hesitate to make a purchase except at a low price, so for the seller, there is a tension between setting high prices and ensuring that there are enough reviews so that buyers can confidently estimate their values. Simultaneously, sellers may use reviews to gauge the demand for items they wish to sell. In this work, we study this pricing problem in an online setting where the seller interacts with a set of buyers of finitely many types, one by one, over a series of $T$ rounds. At each round, the seller first sets a price. Then a buyer arrives and examines the reviews of the previous buyers with the same type, which reveal those buyers' ex-post values. Based on the reviews, the buyer decides to purchase if they have good reason to believe that their ex-ante utility is positive. Crucially, the seller does not know the buyer's type when setting the price, nor even the distribution over types. We provide a no-regret algorithm that the seller can use to obtain high revenue. When there are $d$ types, after $T$ rounds, our algorithm achieves a problem-independent $\tilde O(T^{2/3}d^{1/3})$ regret bound. However, when the smallest probability $q_{\text{min}}$ that any given type appears is large, specifically when $q_{\text{min}} \in Ω(d^{-2/3}T^{-1/3})$, then the same algorithm achieves a $\tilde O(T^{1/2}q_{\text{min}}^{-1/2})$ regret bound. We complement these upper bounds with matching lower bounds in both regimes, showing that our algorithm is minimax optimal up to lower-order terms.

cs.GT↗

arXiv2023

The Sample Complexity of Multi-Distribution Learning for VC Classes

Multi-distribution learning is a natural generalization of PAC learning to settings with multiple data distributions. There remains a significant gap between the known upper and lower bounds for PAC-learnable classes. In particular, though we understand the sample complexity of learning a VC dimension d class on $k$ distributions to be $O(ε^{-2} \ln(k)(d + k) + \min\{ε^{-1} dk, ε^{-4} \ln(k) d\})$, the best lower bound is $Ω(ε^{-2}(d + k \ln(k)))$. We discuss recent progress on this problem and some hurdles that are fundamental to the use of game dynamics in statistical learning.

cs.LG↗

arXiv2023

Jailbroken: How Does LLM Safety Training Fail?

Large language models trained for safety and harmlessness remain susceptible to adversarial misuse, as evidenced by the prevalence of "jailbreak" attacks on early releases of ChatGPT that elicit undesired behavior. Going beyond recognition of the issue, we investigate why such attacks succeed and how they can be created. We hypothesize two failure modes of safety training: competing objectives and mismatched generalization. Competing objectives arise when a model's capabilities and safety goals conflict, while mismatched generalization occurs when safety training fails to generalize to a domain for which capabilities exist. We use these failure modes to guide jailbreak design and then evaluate state-of-the-art models, including OpenAI's GPT-4 and Anthropic's Claude v1.3, against both existing and newly designed attacks. We find that vulnerabilities persist despite the extensive red-teaming and safety-training efforts behind these models. Notably, new attacks utilizing our failure modes succeed on every prompt in a collection of unsafe requests from the models' red-teaming evaluation sets and outperform existing ad hoc jailbreaks. Our analysis emphasizes the need for safety-capability parity -- that safety mechanisms should be as sophisticated as the underlying model -- and argues against the idea that scaling alone can resolve these safety failure modes.

cs.LG↗

arXiv2023

Smoothed Analysis of Sequential Probability Assignment

We initiate the study of smoothed analysis for the sequential probability assignment problem with contexts. We study information-theoretically optimal minmax rates as well as a framework for algorithmic reduction involving the maximum likelihood estimator oracle. Our approach establishes a general-purpose reduction from minimax rates for sequential probability assignment for smoothed adversaries to minimax rates for transductive learning. This leads to optimal (logarithmic) fast rates for parametric classes and classes with finite VC dimension. On the algorithmic front, we develop an algorithm that efficiently taps into the MLE oracle, for general classes of functions. We show that under general conditions this algorithmic approach yields sublinear regret.

cs.LG↗

arXiv2023

Stochastic Minimum Vertex Cover in General Graphs: a $3/2$-Approximation

Our main result is designing an algorithm that returns a vertex cover of $\mathcal{G}^\star$ with size at most $(3/2+ε)$ times the expected size of the minimum vertex cover, using only $O(n/εp)$ non-adaptive queries. This improves over the best-known 2-approximation algorithm by Behnezhad, Blum, and Derakhshan [SODA'22], who also show that $Ω(n/p)$ queries are necessary to achieve any constant approximation. Our guarantees also extend to instances where edge realizations are not fully independent. We complement this upper bound with a tight $3/2$-approximation lower bound for stochastic graphs whose edges realizations demonstrate mild correlations.

cs.DS↗

arXiv2023

Competition, Alignment, and Equilibria in Digital Marketplaces

Competition between traditional platforms is known to improve user utility by aligning the platform's actions with user preferences. But to what extent is alignment exhibited in data-driven marketplaces? To study this question from a theoretical perspective, we introduce a duopoly market where platform actions are bandit algorithms and the two platforms compete for user participation. A salient feature of this market is that the quality of recommendations depends on both the bandit algorithm and the amount of data provided by interactions from users. This interdependency between the algorithm performance and the actions of users complicates the structure of market equilibria and their quality in terms of user utility. Our main finding is that competition in this market does not perfectly align market outcomes with user utility. Interestingly, market outcomes exhibit misalignment not only when the platforms have separate data repositories, but also when the platforms have a shared data repository. Nonetheless, the data sharing assumptions impact what mechanism drives misalignment and also affect the specific form of misalignment (e.g. the quality of the best-case and worst-case market outcomes). More broadly, our work illustrates that competition in digital marketplaces has subtle consequences for user utility that merit further investigation.

cs.GT↗

arXiv2022

Oracle-Efficient Online Learning for Beyond Worst-Case Adversaries

In this paper, we study oracle-efficient algorithms for beyond worst-case analysis of online learning. We focus on two settings. First, the smoothed analysis setting of [RST11,HRS22] where an adversary is constrained to generating samples from distributions whose density is upper bounded by $1/σ$ times the uniform density. Second, the setting of $K$-hint transductive learning, where the learner is given access to $K$ hints per time step that are guaranteed to include the true instance. We give the first known oracle-efficient algorithms for both settings that depend only on the pseudo (or VC) dimension of the class and parameters $σ$ and $K$ that capture the power of the adversary. In particular, we achieve oracle-efficient regret bounds of $ \widetilde{O} ( \sqrt{T dσ^{-1}} ) $ and $ \widetilde{O} ( \sqrt{T dK} ) $ for learning real-valued functions and $ O ( \sqrt{T dσ^{-\frac{1}{2}} } )$ for learning binary-valued functions. For the smoothed analysis setting, our results give the first oracle-efficient algorithm for online learning with smoothed adversaries [HRS22]. This contrasts the computational separation between online learning with worst-case adversaries and offline learning established by [HK16]. Our algorithms also achieve improved bounds for worst-case setting with small domains. In particular, we give an oracle-efficient algorithm with regret of $O ( \sqrt{T(d |\mathcal{X}|)^{1/2} })$, which is a refinement of the earlier $O ( \sqrt{T|\mathcal{X}|})$ bound by [DS16].

cs.LG↗

arXiv2021

Smoothed Analysis with Adaptive Adversaries

We prove novel algorithmic guarantees for several online problems in the smoothed analysis model. In this model, at each time an adversary chooses an input distribution with density function bounded above by $\tfrac{1}σ$ times that of the uniform distribution; nature then samples an input from this distribution. Crucially, our results hold for {\em adaptive} adversaries that can choose an input distribution based on the decisions of the algorithm and the realizations of the inputs in the previous time steps. This paper presents a general technique for proving smoothed algorithmic guarantees against adaptive adversaries, in effect reducing the setting of adaptive adversaries to the simpler case of oblivious adversaries. We apply this technique to prove strong smoothed guarantees for three problems: -Online learning: We consider the online prediction problem, where instances are generated from an adaptive sequence of $σ$-smooth distributions and the hypothesis class has VC dimension $d$. We bound the regret by $\tilde{O}\big(\sqrt{T d\ln(1/σ)} + d\sqrt{\ln(T/σ)}\big)$. This answers open questions of [RST11,Hag18]. -Online discrepancy minimization: We consider the online Komlós problem, where the input is generated from an adaptive sequence of $σ$-smooth and isotropic distributions on the $\ell_2$ unit ball. We bound the $\ell_\infty$ norm of the discrepancy vector by $\tilde{O}\big(\ln^2\!\big( \frac{nT}σ\big) \big)$. -Dispersion in online optimization: We consider online optimization of piecewise Lipschitz functions where functions with $\ell$ discontinuities are chosen by a smoothed adaptive adversary and show that the resulting sequence is $\big( σ/{\sqrt{T\ell}}, \tilde O\big(\sqrt{T\ell} \big)\big)$-dispersed. This matches the parameters of [BDV18] for oblivious adversaries, up to log factors.

cs.LG↗

arXiv2021

One for One, or All for All: Equilibria and Optimality of Collaboration in Federated Learning

In recent years, federated learning has been embraced as an approach for bringing about collaboration across large populations of learning agents. However, little is known about how collaboration protocols should take agents' incentives into account when allocating individual resources for communal learning in order to maintain such collaborations. Inspired by game theoretic notions, this paper introduces a framework for incentive-aware learning and data sharing in federated learning. Our stable and envy-free equilibria capture notions of collaboration in the presence of agents interested in meeting their learning objectives while keeping their own sample collection burden low. For example, in an envy-free equilibrium, no agent would wish to swap their sampling burden with any other agent and in a stable equilibrium, no agent would wish to unilaterally reduce their sampling burden. In addition to formalizing this framework, our contributions include characterizing the structural properties of such equilibria, proving when they exist, and showing how they can be computed. Furthermore, we compare the sample complexity of incentive-aware collaboration with that of optimal collaboration when one ignores agents' incentives.

cs.LG↗

arXiv2020

Noise in Classification

This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount of data. However, even a small amount of adversarial noise makes this problem notoriously hard in the worst-case. We discuss approaches for dealing with these negative results by exploiting natural assumptions on the data-generating process.

cs.LG↗

arXiv2020

Maximizing Welfare with Incentive-Aware Evaluation Mechanisms

Motivated by applications such as college admission and insurance rate determination, we propose an evaluation problem where the inputs are controlled by strategic individuals who can modify their features at a cost. A learner can only partially observe the features, and aims to classify individuals with respect to a quality score. The goal is to design an evaluation mechanism that maximizes the overall quality score, i.e., welfare, in the population, taking any strategic updating into account. We further study the algorithmic aspect of finding the welfare maximizing evaluation mechanism under two specific settings in our model. When scores are linear and mechanisms use linear scoring rules on the observable features, we show that the optimal evaluation mechanism is an appropriate projection of the quality score. When mechanisms must use linear thresholds, we design a polynomial time algorithm with a (1/4)-approximation guarantee when the underlying feature distribution is sufficiently smooth and admits an oracle for finding dense regions. We extend our results to settings where the prior distribution is unknown and must be learned from samples.

cs.GT↗

arXiv2020

Structured Robust Submodular Maximization: Offline and Online Algorithms

Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions obtained via this approach are unstable to perturbations in data defining the submodular functions. Robust submodular maximization has been proposed as a richer model that aims to overcome this discrepancy as well as increase the modeling scope of submodular optimization. In this work, we consider robust submodular maximization with structured combinatorial constraints and give efficient algorithms with provable guarantees. Our approach is applicable to constraints defined by single or multiple matroids, knapsack as well as distributionally robust criteria. We consider both the offline setting where the data defining the problem is known in advance as well as the online setting where the input data is revealed over time. For the offline setting, we give a general (nearly) optimal bi-criteria approximation algorithm that relies on new extensions of classical algorithms for submodular maximization. For the online version of the problem, we give an algorithm that returns a bi-criteria solution with sub-linear regret.

cs.DS↗

arXiv2020

Smoothed Analysis of Online and Differentially Private Learning

Practical and pervasive needs for robustness and privacy in algorithms have inspired the design of online adversarial and differentially private learning algorithms. The primary quantity that characterizes learnability in these settings is the Littlestone dimension of the class of hypotheses [Ben-David et al., 2009, Alon et al., 2019]. This characterization is often interpreted as an impossibility result because classes such as linear thresholds and neural networks have infinite Littlestone dimension. In this paper, we apply the framework of smoothed analysis [Spielman and Teng, 2004], in which adversarially chosen inputs are perturbed slightly by nature. We show that fundamentally stronger regret and error guarantees are possible with smoothed adversaries than with worst-case adversaries. In particular, we obtain regret and privacy error bounds that depend only on the VC dimension and the bracketing number of a hypothesis class, and on the magnitudes of the perturbations.

cs.LG↗

arXiv2019

The Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally

The long-term impact of algorithmic decision making is shaped by the dynamics between the deployed decision rule and individuals' response. Focusing on settings where each individual desires a positive classification---including many important applications such as hiring and school admissions, we study a dynamic learning setting where individuals invest in a positive outcome based on their group's expected gain and the decision rule is updated to maximize institutional benefit. By characterizing the equilibria of these dynamics, we show that natural challenges to desirable long-term outcomes arise due to heterogeneity across groups and the lack of realizability. We consider two interventions, decoupling the decision rule by group and subsidizing the cost of investment. We show that decoupling achieves optimal outcomes in the realizable case but has discrepant effects that may depend on the initial conditions otherwise. In contrast, subsidizing the cost of investment is shown to create better equilibria for the disadvantaged group even in the absence of realizability.

cs.GT↗

arXiv2019

Oracle-Efficient Online Learning and Auction Design

We consider the design of computationally efficient online learning algorithms in an adversarial setting in which the learner has access to an offline optimization oracle. We present an algorithm called Generalized Follow-the-Perturbed-Leader and provide conditions under which it is oracle-efficient while achieving vanishing regret. Our results make significant progress on an open problem raised by Hazan and Koren, who showed that oracle-efficient algorithms do not exist in general and asked whether one can identify properties under which oracle-efficient online learning may be possible. Our auction-design framework considers an auctioneer learning an optimal auction for a sequence of adversarially selected valuations with the goal of achieving revenue that is almost as good as the optimal auction in hindsight, among a class of auctions. We give oracle-efficient learning results for: (1) VCG auctions with bidder-specific reserves in single-parameter settings, (2) envy-free item pricing in multi-item auctions, and (3) s-level auctions of Morgenstern and Roughgarden for single-item settings. The last result leads to an approximation of the overall optimal Myerson auction when bidders' valuations are drawn according to a fast-mixing Markov process, extending prior work that only gave such guarantees for the i.i.d. setting. Finally, we derive various extensions, including: (1) oracle-efficient algorithms for the contextual learning setting in which the learner has access to side information (such as bidder demographics), (2) learning with approximate oracles such as those based on Maximal-in-Range algorithms, and (3) no-regret bidding in simultaneous auctions, resolving an open problem of Daskalakis and Syrgkanis.

cs.LG↗

arXiv2019

Toward a Characterization of Loss Functions for Distribution Learning

In this work we study loss functions for learning and evaluating probability distributions over large discrete domains. Unlike classification or regression where a wide variety of loss functions are used, in the distribution learning and density estimation literature, very few losses outside the dominant $log\ loss$ are applied. We aim to understand this fact, taking an axiomatic approach to the design of loss functions for learning distributions. We start by proposing a set of desirable criteria that any good loss function should satisfy. Intuitively, these criteria require that the loss function faithfully evaluates a candidate distribution, both in expectation and when estimated on a few samples. Interestingly, we observe that \emph{no loss function} possesses all of these criteria. However, one can circumvent this issue by introducing a natural restriction on the set of candidate distributions. Specifically, we require that candidates are $calibrated$ with respect to the target distribution, i.e., they may contain less information than the target but otherwise do not significantly distort the truth. We show that, after restricting to this set of distributions, the log loss, along with a large variety of other losses satisfy the desired criteria. These results pave the way for future investigations of distribution learning that look beyond the log loss, choosing a loss function based on application or domain need.

cs.LG↗

arXiv2018

$k$-center Clustering under Perturbation Resilience

The $k$-center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case instances. Therefore to improve on these ratios, one must go beyond the worst case. In this work, we take this approach and provide strong positive results both for the asymmetric and symmetric $k$-center problems under a natural input stability (promise) condition called $α$-perturbation resilience [Bilu and Linia 2012], which states that the optimal solution does not change under any alpha-factor perturbation to the input distances. We provide algorithms that give strong guarantees simultaneously for stable and non-stable instances: our algorithms always inherit the worst-case guarantees of clustering approximation algorithms, and output the optimal solution if the input is $2$-perturbation resilient. Furthermore, we prove our result is tight by showing symmetric $k$-center under $(2-ε)$-perturbation resilience is hard unless $NP=RP$. The impact of our results are multifaceted. This is the first tight result for any problem under perturbation resilience. Furthermore, our results illustrate a surprising relationship between symmetric and asymmetric $k$-center instances under perturbation resilience. Unlike approximation ratio, for which symmetric $k$-center is easily solved to a factor of 2 but asymmetric $k$-center cannot be approximated to any constant factor, both symmetric and asymmetric $k$-center can be solved optimally under resilience to 2-perturbations. Finally, our guarantees in the setting where only part of the data satisfies perturbation resilience makes these algorithms more applicable to real-life instances.

cs.DS↗

arXiv2017

The Provable Virtue of Laziness in Motion Planning

The Lazy Shortest Path (LazySP) class consists of motion-planning algorithms that only evaluate edges along shortest paths between the source and target. These algorithms were designed to minimize the number of edge evaluations in settings where edge evaluation dominates the running time of the algorithm; but how close to optimal are LazySP algorithms in terms of this objective? Our main result is an analytical upper bound, in a probabilistic model, on the number of edge evaluations required by LazySP algorithms; a matching lower bound shows that these algorithms are asymptotically optimal in the worst case.

cs.RO↗