Alireza Fallah

Federico Echenique, Alireza Fallah, Baihe Huang et al.

Aligning large language models (LLMs) to human preferences typically relies on aggregating pooled feedback into a single reward model. However, this standard approach assumes that all labelers share the same underlying preferences, ignoring the fact that real-world labelers are highly heterogeneous and usually anonymous. Consequently, relying solely on binary choice data fundamentally distorts the learned policy, making the true population-average preference unidentifiable. To overcome this critical limitation, we demonstrate that augmenting preference datasets with a simple, secondary signal -- the user's response time -- can restore the identifiability of the population's average preference. By modeling each decision as a Drift-Diffusion Model (DDM), we introduce a novel, consistent estimator of heterogeneous preferences that successfully corrects the distortions of standard choice-only labels. We prove that our estimator asymptotically converges to the true average preference even in extreme cases where each anonymous labeler contributes only a single choice. Empirically, across both synthetic and real-world datasets, our method consistently outperforms standard baselines that otherwise fail and plateau at a bias floor. Because response times are essentially free to record and require zero user tracking or identification, our results bring promises and open up new opportunities for future data-collection pipelines to improve the social benefit without requiring user-level identifiers or repeated elicitations.

Maryam Aliakbarpour, Syomantak Chaudhuri, Thomas A. Courtade et al.

Local Differential Privacy (LDP) offers strong privacy guarantees without requiring users to trust external parties. However, LDP applies uniform protection to all data features, including less sensitive ones, which degrades performance of downstream tasks. To overcome this limitation, we propose a Bayesian framework, Bayesian Coordinate Differential Privacy (BCDP), that enables feature-specific privacy quantification. This more nuanced approach complements LDP by adjusting privacy protection according to the sensitivity of each feature, enabling improved performance of downstream tasks without compromising privacy. We characterize the properties of BCDP and articulate its connections with standard non-Bayesian privacy frameworks. We further apply our BCDP framework to the problems of private mean estimation and ordinary least-squares regression. The BCDP-based approach obtains improved accuracy compared to a purely LDP-based approach, without compromising on privacy.

Maryam Aliakbarpour, Alireza Fallah, Swaha Roy et al.

We study statistical estimation under local differential privacy (LDP) when users may hold heterogeneous privacy levels and accuracy must be guaranteed with high probability. Departing from the common in-expectation analyses, and for one-dimensional and multi-dimensional mean estimation problems, we develop finite sample upper bounds in $\ell_2$-norm that hold with probability at least $1-β$. We complement these results with matching minimax lower bounds, establishing the optimality (up to constants) of our guarantees in the heterogeneous LDP regime. We further study distribution learning in $\ell_\infty$-distance, designing an algorithm with high-probability guarantees under heterogeneous privacy demands. Our techniques offer principled guidance for designing mechanisms in settings with user-specific privacy levels.

Alireza Fallah, Michael I. Jordan, Annie Ulichney

Machine learning models must balance accuracy and fairness, but these goals often conflict, particularly when data come from multiple demographic groups. A useful tool for understanding this trade-off is the fairness-accuracy (FA) frontier, which characterizes the set of models that cannot be simultaneously improved in both fairness and accuracy. Prior analyses of the FA frontier provide a full characterization under the assumption of complete knowledge of population distributions -- an unrealistic ideal. We study the FA frontier in the finite-sample regime, showing how it deviates from its population counterpart and quantifying the worst-case gap between them. In particular, we derive minimax-optimal estimators that depend on the designer's knowledge of the covariate distribution. For each estimator, we characterize how finite-sample effects asymmetrically impact each group's risk, and identify optimal sample allocation strategies. Our results transform the FA frontier from a theoretical construct into a practical tool for policymakers and practitioners who must often design algorithms with limited data.

Federico Echenique, Alireza Fallah, Michael I. Jordan

We propose a general methodology for recovering preference parameters from data on choices and response times. Our methods yield estimates with fast ($1/n$ for $n$ data points) convergence rates when specialized to the popular Drift Diffusion Model (DDM), but are broadly applicable to generalizations of the DDM as well as to alternative models of decision making that make use of response time data. The paper develops an empirical application to an experiment on intertemporal choice, showing that the use of response times delivers predictive accuracy and matters for the estimation of economically relevant parameters.

Alireza Fallah, Ali Makhdoumi, Azarakhsh Malekian et al.

We consider a platform's problem of collecting data from privacy sensitive users to estimate an underlying parameter of interest. We formulate this question as a Bayesian-optimal mechanism design problem, in which an individual can share her (verifiable) data in exchange for a monetary reward or services, but at the same time has a (private) heterogeneous privacy cost which we quantify using differential privacy. We consider two popular differential privacy settings for providing privacy guarantees for the users: central and local. In both settings, we establish minimax lower bounds for the estimation error and derive (near) optimal estimators for given heterogeneous privacy loss levels for users. Building on this characterization, we pose the mechanism design problem as the optimal selection of an estimator and payments that will elicit truthful reporting of users' privacy sensitivities. Under a regularity condition on the distribution of privacy sensitivities we develop efficient algorithmic mechanisms to solve this problem in both privacy settings. Our mechanism in the central setting can be implemented in time $\mathcal{O}(n \log n)$ where $n$ is the number of users and our mechanism in the local setting admits a Polynomial Time Approximation Scheme (PTAS).

Hilal Asi, John Duchi, Alireza Fallah et al.

We study adaptive methods for differentially private convex optimization, proposing and analyzing differentially private variants of a Stochastic Gradient Descent (SGD) algorithm with adaptive stepsizes, as well as the AdaGrad algorithm. We provide upper bounds on the regret of both algorithms and show that the bounds are (worst-case) optimal. As a consequence of our development, we show that our private versions of AdaGrad outperform adaptive SGD, which in turn outperforms traditional SGD in scenarios with non-isotropic gradients where (non-private) Adagrad provably outperforms SGD. The major challenge is that the isotropic noise typically added for privacy dominates the signal in gradient geometry for high-dimensional problems; approaches to this that effectively optimize over lower-dimensional subspaces simply ignore the actual problems that varying gradient geometries introduce. In contrast, we study non-isotropic clipping and noise addition, developing a principled theoretical approach; the consequent procedures also enjoy significantly stronger empirical performance than prior approaches.

Theo Diamandis, Yonina C. Eldar, Alireza Fallah et al.

Multi-modal distributions are commonly used to model clustered data in statistical learning tasks. In this paper, we consider the Mixed Linear Regression (MLR) problem. We propose an optimal transport-based framework for MLR problems, Wasserstein Mixed Linear Regression (WMLR), which minimizes the Wasserstein distance between the learned and target mixture regression models. Through a model-based duality analysis, WMLR reduces the underlying MLR task to a nonconvex-concave minimax optimization problem, which can be provably solved to find a minimax stationary point by the Gradient Descent Ascent (GDA) algorithm. In the special case of mixtures of two linear regression models, we show that WMLR enjoys global convergence and generalization guarantees. We prove that WMLR's sample complexity grows linearly with the dimension of data. Finally, we discuss the application of WMLR to the federated learning task where the training samples are collected by multiple agents in a network. Unlike the Expectation Maximization algorithm, WMLR directly extends to the distributed, federated learning setting. We support our theoretical results through several numerical experiments, which highlight our framework's ability to handle the federated learning setting with mixture models.

Alireza Fallah, Aryan Mokhtari, Asuman Ozdaglar

In this paper, we study the generalization properties of Model-Agnostic Meta-Learning (MAML) algorithms for supervised learning problems. We focus on the setting in which we train the MAML model over $m$ tasks, each with $n$ data points, and characterize its generalization error from two points of view: First, we assume the new task at test time is one of the training tasks, and we show that, for strongly convex objective functions, the expected excess population loss is bounded by ${\mathcal{O}}(1/mn)$. Second, we consider the MAML algorithm's generalization to an unseen task and show that the resulting generalization error depends on the total variation distance between the underlying distributions of the new task and the tasks observed during the training process. Our proof techniques rely on the connections between algorithmic stability and generalization bounds of algorithms. In particular, we propose a new definition of stability for meta-learning algorithms, which allows us to capture the role of both the number of tasks $m$ and number of samples per task $n$ on the generalization error of MAML.

Alireza Fallah, Aryan Mokhtari, Asuman Ozdaglar

In Federated Learning, we aim to train models across multiple computing units (users), while users can only communicate with a common central server, without exchanging their data samples. This mechanism exploits the computational power of all users and allows users to obtain a richer model as their models are trained over a larger set of data points. However, this scheme only develops a common output for all the users, and, therefore, it does not adapt the model to each user. This is an important missing feature, especially given the heterogeneity of the underlying data distribution for various users. In this paper, we study a personalized variant of the federated learning in which our goal is to find an initial shared model that current or new users can easily adapt to their local dataset by performing one or a few steps of gradient descent with respect to their own data. This approach keeps all the benefits of the federated learning architecture, and, by structure, leads to a more personalized model for each user. We show this problem can be studied within the Model-Agnostic Meta-Learning (MAML) framework. Inspired by this connection, we study a personalized variant of the well-known Federated Averaging algorithm and evaluate its performance in terms of gradient norm for non-convex loss functions. Further, we characterize how this performance is affected by the closeness of underlying distributions of user data, measured in terms of distribution distances such as Total Variation and 1-Wasserstein metric.

Alireza Fallah, Asuman Ozdaglar, Sarath Pattathil

In this paper, we study the minimax optimization problem in the smooth and strongly convex-strongly concave setting when we have access to noisy estimates of gradients. In particular, we first analyze the stochastic Gradient Descent Ascent (GDA) method with constant stepsize, and show that it converges to a neighborhood of the solution of the minimax problem. We further provide tight bounds on the convergence rate and the size of this neighborhood. Next, we propose a multistage variant of stochastic GDA (M-GDA) that runs in multiple stages with a particular learning rate decay schedule and converges to the exact solution of the minimax problem. We show M-GDA achieves the lower bounds in terms of noise dependence without any assumptions on the knowledge of noise characteristics. We also show that M-GDA obtains a linear decay rate with respect to the error's dependence on the initial error, although the dependence on condition number is suboptimal. In order to improve this dependence, we apply the multistage machinery to the stochastic Optimistic Gradient Descent Ascent (OGDA) algorithm and propose the M-OGDA algorithm which also achieves the optimal linear decay rate with respect to the initial error. To the best of our knowledge, this method is the first to simultaneously achieve the best dependence on noise characteristic as well as the initial error and condition number.

Alireza Fallah, Kristian Georgiev, Aryan Mokhtari et al.

We consider Model-Agnostic Meta-Learning (MAML) methods for Reinforcement Learning (RL) problems, where the goal is to find a policy using data from several tasks represented by Markov Decision Processes (MDPs) that can be updated by one step of stochastic policy gradient for the realized MDP. In particular, using stochastic gradients in MAML update steps is crucial for RL problems since computation of exact gradients requires access to a large number of possible trajectories. For this formulation, we propose a variant of the MAML method, named Stochastic Gradient Meta-Reinforcement Learning (SG-MRL), and study its convergence properties. We derive the iteration and sample complexity of SG-MRL to find an $ε$-first-order stationary point, which, to the best of our knowledge, provides the first convergence guarantee for model-agnostic meta-reinforcement learning algorithms. We further show how our results extend to the case where more than one step of stochastic policy gradient method is used at test time. Finally, we empirically compare SG-MRL and MAML in several deep RL environments.

Alireza Fallah, Mert Gurbuzbalaban, Asuman Ozdaglar et al.

We study distributed stochastic gradient (D-SG) method and its accelerated variant (D-ASG) for solving decentralized strongly convex stochastic optimization problems where the objective function is distributed over several computational units, lying on a fixed but arbitrary connected communication graph, subject to local communication constraints where noisy estimates of the gradients are available. We develop a framework which allows to choose the stepsize and the momentum parameters of these algorithms in a way to optimize performance by systematically trading off the bias, variance, robustness to gradient noise and dependence to network effects. When gradients do not contain noise, we also prove that distributed accelerated methods can \emph{achieve acceleration}, requiring $\mathcal{O}(κ\log(1/\varepsilon))$ gradient evaluations and $\mathcal{O}(κ\log(1/\varepsilon))$ communications to converge to the same fixed point with the non-accelerated variant where $κ$ is the condition number and $\varepsilon$ is the target accuracy. To our knowledge, this is the first acceleration result where the iteration complexity scales with the square root of the condition number in the context of \emph{primal} distributed inexact first-order methods. For quadratic functions, we also provide finer performance bounds that are tight with respect to bias and variance terms. Finally, we study a multistage version of D-ASG with parameters carefully varied over stages to ensure exact $\mathcal{O}(-k/\sqrtκ)$ linear decay in the bias term as well as optimal $\mathcal{O}(σ^2/k)$ in the variance term. We illustrate through numerical experiments that our approach results in practical algorithms that are robust to gradient noise and that can outperform existing methods.

Alireza Fallah, Aryan Mokhtari, Asuman Ozdaglar

We study the convergence of a class of gradient-based Model-Agnostic Meta-Learning (MAML) methods and characterize their overall complexity as well as their best achievable accuracy in terms of gradient norm for nonconvex loss functions. We start with the MAML method and its first-order approximation (FO-MAML) and highlight the challenges that emerge in their analysis. By overcoming these challenges not only we provide the first theoretical guarantees for MAML and FO-MAML in nonconvex settings, but also we answer some of the unanswered questions for the implementation of these algorithms including how to choose their learning rate and the batch size for both tasks and datasets corresponding to tasks. In particular, we show that MAML can find an $ε$-first-order stationary point ($ε$-FOSP) for any positive $ε$ after at most $\mathcal{O}(1/ε^2)$ iterations at the expense of requiring second-order information. We also show that FO-MAML which ignores the second-order information required in the update of MAML cannot achieve any small desired level of accuracy, i.e., FO-MAML cannot find an $ε$-FOSP for any $ε>0$. We further propose a new variant of the MAML algorithm called Hessian-free MAML which preserves all theoretical guarantees of MAML, without requiring access to second-order information.

Necdet Serhat Aybat, Alireza Fallah, Mert Gurbuzbalaban et al.

We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal rate both in the deterministic and stochastic case and operates without knowledge of noise characteristics. The algorithm consists of stages that use a stochastic version of Nesterov's method with a specific restart and parameters selected to achieve the fastest reduction in the bias-variance terms in the convergence rate bounds.

Necdet Serhat Aybat, Alireza Fallah, Mert Gurbuzbalaban et al.

We study the trade-offs between convergence rate and robustness to gradient errors in designing a first-order algorithm. We focus on gradient descent (GD) and accelerated gradient (AG) methods for minimizing strongly convex functions when the gradient has random errors in the form of additive white noise. With gradient errors, the function values of the iterates need not converge to the optimal value; hence, we define the robustness of an algorithm to noise as the asymptotic expected suboptimality of the iterate sequence to input noise power. For this robustness measure, we provide exact expressions for the quadratic case using tools from robust control theory and tight upper bounds for the smooth strongly convex case using Lyapunov functions certified through matrix inequalities. We use these characterizations within an optimization problem which selects parameters of each algorithm to achieve a particular trade-off between rate and robustness. Our results show that AG can achieve acceleration while being more robust to random gradient errors. This behavior is quite different than previously reported in the deterministic gradient noise setting. We also establish some connections between the robustness of an algorithm and how quickly it can converge back to the optimal solution if it is perturbed from the optimal point with deterministic noise. Our framework also leads to practical algorithms that can perform better than other state-of-the-art methods in the presence of random gradient noise.