Sanjeev Kulkarni

Aaradhya Pandey, Sanjeev Kulkarni

Machine learning systems increasingly face requirements to forget not only individual data points, but entire domains of information, such as toxic language, copyrighted corpora, or demographic biases. This raises a fundamental dilemma of statistical-computational tradeoffs: removing all samples from an unwanted domain may be computationally prohibitive, while randomly removing a subset may not provide distribution-level statistical guarantees. We propose a statistical framework for distributional unlearning, in which domains are modeled as probability distributions, and the goal is to remove a carefully chosen subset of samples that reduces the effect of an unwanted distribution while preserving performance on a desired one. We formalize this using a hypothesis test of the edited data with the desired and unwanted domains, leading to an interpretable and robust criterion for selecting samples to remove. Within this statistical framework, we characterize the fundamental region of the allowable edited data distributions and the removal-preservation Pareto frontier for a broad class of distribution families. This includes parametric families such as shifted Gaussians of arbitrary dimension, a one-dimensional location family with log-concave noise, and the one-dimensional Poisson family. It also includes nonparametric families such as the Gaussian white noise model, a canonical model for nonparametric regression. We prove composition rules that describe how distributional unlearning behaves across multimodal unwanted domains, and introduce a central-limit behavior for the removal-preservation baselines when composing a large number of such families. Finally, we provide finite sample guarantees by providing Pareto frontiers for some selection algorithms, and observe an information-computation gap.

Zhixu Tao, Rajita Chandak, Sanjeev Kulkarni

Data heterogeneity has been a long-standing bottleneck in studying the convergence rates of Federated Learning algorithms. In order to better understand the issue of data heterogeneity, we study the convergence rate of the Expectation-Maximization (EM) algorithm for the Federated Mixture of $K$ Linear Regressions model (FMLR). We completely characterize the convergence rate of the EM algorithm under all regimes of $m/n$ where $m$ is the number of clients and $n$ is the number of data points per client. We show that with a signal-to-noise-ratio (SNR) of order $Ω(\sqrt{K})$, the well-initialized EM algorithm converges within the minimax distance of the ground truth under all regimes. Interestingly, we identify that when the number of clients grows reasonably with respect to the number of data points per client, the EM algorithm only requires a constant number of iterations to converge. We perform experiments on synthetic data to illustrate our results. In line with our theoretical findings, the simulations show that rather than being a bottleneck, data heterogeneity can accelerate the convergence of iterative federated algorithms.

Arman Adibi, Nicolo Dal Fabbro, Luca Schenato et al.

Motivated by applications in large-scale and multi-agent reinforcement learning, we study the non-asymptotic performance of stochastic approximation (SA) schemes with delayed updates under Markovian sampling. While the effect of delays has been extensively studied for optimization, the manner in which they interact with the underlying Markov process to shape the finite-time performance of SA remains poorly understood. In this context, our first main contribution is to show that under time-varying bounded delays, the delayed SA update rule guarantees exponentially fast convergence of the \emph{last iterate} to a ball around the SA operator's fixed point. Notably, our bound is \emph{tight} in its dependence on both the maximum delay $τ_{max}$, and the mixing time $τ_{mix}$. To achieve this tight bound, we develop a novel inductive proof technique that, unlike various existing delayed-optimization analyses, relies on establishing uniform boundedness of the iterates. As such, our proof may be of independent interest. Next, to mitigate the impact of the maximum delay on the convergence rate, we provide the first finite-time analysis of a delay-adaptive SA scheme under Markovian sampling. In particular, we show that the exponent of convergence of this scheme gets scaled down by $τ_{avg}$, as opposed to $τ_{max}$ for the vanilla delayed SA rule; here, $τ_{avg}$ denotes the average delay across all iterations. Moreover, the adaptive scheme requires no prior knowledge of the delay sequence for step-size tuning. Our theoretical findings shed light on the finite-time effects of delays for a broad class of algorithms, including TD learning, Q-learning, and stochastic gradient descent under Markovian sampling.

Zhixu Silvia Tao, Ian Mason, Sanjeev Kulkarni et al.

Task Arithmetic is a model merging technique that enables the combination of multiple models' capabilities into a single model through simple arithmetic in the weight space, without the need for additional fine-tuning or access to the original training data. However, the factors that determine the success of Task Arithmetic remain unclear. In this paper, we examine Task Arithmetic for multi-task learning by framing it as a one-shot Federated Learning problem. We demonstrate that Task Arithmetic is mathematically equivalent to the commonly used algorithm in Federated Learning, called Federated Averaging (FedAvg). By leveraging well-established theoretical results from FedAvg, we identify two key factors that impact the performance of Task Arithmetic: data heterogeneity and training heterogeneity. To mitigate these challenges, we adapt several algorithms from Federated Learning to improve the effectiveness of Task Arithmetic. Our experiments demonstrate that applying these algorithms can often significantly boost performance of the merged model compared to the original Task Arithmetic approach. This work bridges Task Arithmetic and Federated Learning, offering new theoretical perspectives on Task Arithmetic and improved practical methodologies for model merging.

Melda Alaluf, Giulia Crippa, Sinong Geng et al.

We study paycheck optimization, which examines how to allocate income in order to achieve several competing financial goals. For paycheck optimization, a quantitative methodology is missing, due to a lack of a suitable problem formulation. To deal with this issue, we formulate the problem as a utility maximization problem. The proposed formulation is able to (i) unify different financial goals; (ii) incorporate user preferences regarding the goals; (iii) handle stochastic interest rates. The proposed formulation also facilitates an end-to-end reinforcement learning solution, which is implemented on a variety of problem settings.

Aaradhya Pandey, Arnab Auddy, Haolin Zou et al.

Machine unlearning seeks to efficiently remove the influence of selected data while preserving generalization. Significant progress has been made in low dimensions $(p \ll n)$, but high dimensions pose serious theoretical challenges as standard optimization assumptions of $Ω(1)$ strong convexity and $O(1)$ smoothness of the per-example loss $f$ rarely hold simultaneously in proportional regimes $(p\sim n)$. In this work, we introduce $\varepsilon$-Gaussian certifiability, a canonical and robust notion well-suited to high-dimensional regimes, that optimally captures a broad class of noise adding mechanisms. Then we theoretically analyze the performance of a widely used unlearning algorithm based on one step of the Newton method in the high-dimensional setting described above. Our analysis shows that a single Newton step, followed by a well-calibrated Gaussian noise, is sufficient to achieve both privacy and accuracy in this setting. This result stands in sharp contrast to the only prior work that analyzes machine unlearning in high dimensions \citet{zou2025certified}, which relaxes some of the standard optimization assumptions for high-dimensional applicability, but operates under the notion of $\varepsilon$-certifiability. That work concludes %that a single Newton step is insufficient even for removing a single data point, and that at least two steps are required to ensure both privacy and accuracy. Our result leads us to conclude that the discrepancy in the number of steps arises because of the sub optimality of the notion of $\varepsilon$-certifiability and its incompatibility with noise adding mechanisms, which $\varepsilon$-Gaussian certifiability is able to overcome optimally.

Xiang Ji, Sanjeev Kulkarni, Mengdi Wang et al.

This work studies the challenge of aligning large language models (LLMs) with offline preference data. We focus on alignment by Reinforcement Learning from Human Feedback (RLHF) in particular. While popular preference optimization methods exhibit good empirical performance in practice, they are not theoretically guaranteed to converge to the optimal policy and can provably fail when the data coverage is sparse by classical offline reinforcement learning (RL) results. On the other hand, a recent line of work has focused on theoretically motivated preference optimization methods with provable guarantees, but these are not computationally efficient for large-scale applications like LLM alignment. To bridge this gap, we propose SPAC, a new offline preference optimization method with self-play, inspired by the on-average pessimism technique from the offline RL literature, to be the first provable and scalable approach to LLM alignment. We both provide theoretical analysis for its convergence under single-policy concentrability for the general function approximation setting and demonstrate its competitive empirical performance for LLM alignment on a 7B Mistral model with Open LLM Leaderboard evaluations.

Arun Kejariwal, Sanjeev Kulkarni, Karthik Ramasamy

Velocity is one of the 4 Vs commonly used to characterize Big Data. In this regard, Forrester remarked the following in Q3 2014: "The high velocity, white-water flow of data from innumerable real-time data sources such as market data, Internet of Things, mobile, sensors, click-stream, and even transactions remain largely unnavigated by most firms. The opportunity to leverage streaming analytics has never been greater." Example use cases of streaming analytics include, but not limited to: (a) visualization of business metrics in real-time (b) facilitating highly personalized experiences (c) expediting response during emergencies. Streaming analytics is extensively used in a wide variety of domains such as healthcare, e-commerce, financial services, telecommunications, energy and utilities, manufacturing, government and transportation. In this tutorial, we shall present an in-depth overview of streaming analytics - applications, algorithms and platforms - landscape. We shall walk through how the field has evolved over the last decade and then discuss the current challenges - the impact of the other three Vs, viz., Volume, Variety and Veracity, on Big Data streaming analytics. The tutorial is intended for both researchers and practitioners in the industry. We shall also present state-of-the-affairs of streaming analytics at Twitter.

Emmanuel Abbe, Sanjeev Kulkarni, Eun Jee Lee

This paper develops upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit nonbacktracking walks, Fortuin-Kasteleyn-Ginibre (FKG) type inequalities, and are computed by message passing implementation. Nonbacktracking walks have recently allowed for headways in community detection, and this paper shows that their use can also impact the influence computation. Further, we provide a knob to control the trade-off between the efficiency and the accuracy of the bounds. Finally, the tightness of the bounds is illustrated with simulations on various network models.

Shang Shang, Tiance Wang, Paul Cuff et al.

The potential risk of privacy leakage prevents users from sharing their honest opinions on social platforms. This paper addresses the problem of privacy preservation if the query returns the histogram of rankings. The framework of differential privacy is applied to rank aggregation. The error probability of the aggregated ranking is analyzed as a result of noise added in order to achieve differential privacy. Upper bounds on the error rates for any positional ranking rule are derived under the assumption that profiles are uniformly distributed. Simulation results are provided to validate the probabilistic analysis.