arXiv subjects

Lalitha Sankar

Publications and source records attributed to Lalitha Sankar.

At least 19 recordsLinked to original sources

arXiv2026

DER Allocation without Load Prediction via Reinforcement Learning

The growing variability of renewable generation increases the need for fast and flexible grid-balancing mechanisms. Existing frameworks for distributed energy resource aggregations (DERAs) rely on short-term forecasts of net demand, making their performance highly sensitive to prediction errors. In this paper we present a forecast-free reinforcement learning (RL) framework for DERA allocation that learns optimal policies directly from operational data. We model the DERA dynamics as a deterministic linear system and the exogenous net load as a feature-based linear Markov process, capturing short-range temporal dependencies without explicit forecasting. We derive a closed-form expression for the optimal policy, which is learned through a least-squares value iteration (LSVI) algorithm using data collected across episodes. The proposed framework preserves the interpretability and constraint satisfaction of DER model while adapting to stochastic demand variations through data-driven updates. Numerical experiments on real California Independent System Operator (CAISO) net-demand data demonstrate that the learned controller achieves high tracking accuracy and stable regulation across heterogeneous DER aggregators without requiring any demand prediction.

eess.SY↗

arXiv2026

Forecast and Model Predictive Control of Distributed Energy Resource Aggregators for Net-Demand Balancing

With the rapid demand for energy, even the incorporation of bulk renewable energy sources is not entirely sufficient to meet demand besides adding supply uncertainty. Distributed Energy Resource Aggregators (DERAs) have the potential to address this uncertainty via aggregation and control of decentralized distributed energy sources, thereby acting like virtual power plants. We present a new approach that combines forecasting and model-predictive control to assign DERAs to follow net-demand patterns, while accounting for the dynamics of the aggregate energy sources and their capacity limits. Each DERA is represented as a flexible ``virtual battery" with constraints on state-of-charge and power limits. The dispatch problem is set up as a long-term model predictive control task that aims to minimize differences from desired charge levels, output ramping, and net-load tracking errors. To keep operations efficient in real time, we implement a rolling-horizon MPC, which updates decisions regularly using the latest marginal-demand forecasts. For forecasting, we present two models: linear regression and long-short term memory (LSTM) neural network. Using high-resolution CAISO net-demand data and five typical DERA types, our simulations demonstrate how well our approach tracks marginal-demand; in particular, we highlight the tradeoffs between forecasting horizon times and MPC update rate as well as the dependence on the choice of the load forecasting model. Our results also indicate a slight edge for LSTM models over linear regression for desired time shifts and horizon choices.

eess.SY↗

arXiv2026

DP-MacAdam: Differentially Private Mechanism with Adaptive Clipping and Adaptive Momentum

Differentially private stochastic gradient descent (DP-SGD) has become the standard framework for privacy-preserving machine learning, yet its reliance on a fixed gradient clipping threshold to limit sensitivity remains a significant practical limitation. Adaptive clipping algorithms such as AdaClip shift and scale the gradient prior to clipping and adding noise so that the clipped gradient yields a more informative descent direction. The shift and scaling parameters are selected adaptively based on the empirical mean and variance. However, in existing adaptive clipping algorithms, these empirical estimates have not been also used for momentum to accelerate training itself. On the other hand, DP-Adam is an algorithm that exploits Adam-like momentum updates based on the gradient mean and variance to accelerate training, but does not exploit these estimates for adaptive clipping. In this work, we propose Differentially Private Mechanism with Adaptive Clipping and Adaptive Momentum (DP-MacAdam), a novel algorithm that combines these two approaches so as to use the same mean and variance estimates for both clipping and momentum. We perform an analysis showing that DP-MacAdam estimates the gradient variances in a bias-free manner. In addition, we empirically evaluate the privacy and accuracy of DP-MacAdam, demonstrating that it achieves improved model utility compared to DP-SGD, AdaClip, and DP-Adam baselines, without requiring manual tuning of the clipping threshold.

cs.LG↗

arXiv2026

Correcting Class Imbalance in Prior-Data Fitted Networks for Tabular Classification

Prior-data fitted networks (PFNs) have achieved exceptional performance on tabular classification tasks. However, like other classifiers, their performance can suffer under the effect of class imbalance, resulting in poor performance for rare classes. Several techniques exist which attempt to mitigate the deleterious effect of class imbalance on classification performance, but the in-context learning (ICL) dynamic of PFNs means that loss-based strategies are impossible, and other techniques are unproven. We have adapted several classical techniques addressing class imbalance and analyzed their performance on PFN classification. We observe that thresholding performs exceptionally well because of the calibration characteristics of PFNs, and downsampling performs comparably because of PFNs exceptional limited-data performance, with the additional benefit of reduced computation cost for inference.

cs.LG↗

arXiv2026

ArcMark: Distortion-Free Multi-Byte LLM Watermark via Optimal Transport

Watermarking is an important tool for promoting the responsible use of large language models (LLMs). Existing watermarks insert a signal into generated tokens that either flags LLM-generated text (zero-bit watermarking) or encodes more complex messages (multi-bit watermarking). Though a number of recent approaches insert multiple bits into text without perturbing average next-token predictions, they largely extend design principles from the zero-bit setting, such as encoding a single bit per token. In contrast, a watermarker capable of embedding multiple bytes into the text would dramatically increase the potential applications, by embedding information such as the ID of the user who submitted the prompt, the precise model version that was used, or even the prompt itself. We address this problem by introducing ArcMark: a new watermark construction based on coding and information-theoretic principles that is capable of reliably embedding multiple bytes of information into just a few hundred tokens, without any distortion of the underlying LLM next-token distribution. We derive ArcMark by formulating the distortion-free watermarking problem as a channel coding problem, and deriving an information-theoretic channel capacity that establishes the fundamental limit of embedding information in LLM output in a distortion-free manner. This capacity formulation informs the design of ArcMark. In practice, ArcMark outperforms competing multi-bit distortion-free watermarks in terms of reconstruction accuracy, including in the face of attacks that alter a subset of the LLM text. ArcMark output is also shown to be indistinguishable from unwatermarked text in terms of perplexity, and in downstream task quality.

cs.LG↗

arXiv2025

An information theorist's tour of differential privacy

Since being proposed in 2006, differential privacy has become a standard method for quantifying certain risks in publishing or sharing analyses of sensitive data. At its heart, differential privacy measures risk in terms of the differences between probability distributions, which is a central topic in information theory. A differentially private algorithm is a channel between the underlying data and the output of the analysis. Seen in this way, the guarantees made by differential privacy can be understood in terms of properties of this channel. In this article we examine a few of the key connections between information theory and the formulation/application of differential privacy, giving an ``operational significance'' for relevant information measures.

cs.IT↗

arXiv2025

Linear Dynamics meets Linear MDPs: Closed-Form Optimal Policies via Reinforcement Learning

Many applications -- including power systems, robotics, and economics -- involve a dynamical system interacting with a stochastic and hard-to-model environment. We adopt a reinforcement learning approach to control such systems. Specifically, we consider a deterministic, discrete-time, linear, time-invariant dynamical system coupled with a feature-based linear Markov process with an unknown transition kernel. The objective is to learn a control policy that optimizes a quadratic cost over the system state, the Markov process, and the control input. Leveraging both components of the system, we derive an explicit parametric form for the optimal state-action value function and the corresponding optimal policy. Our model is distinct in combining aspects of both classical Linear Quadratic Regulator (LQR) and linear Markov decision process (MDP) frameworks. This combination retains the implementation simplicity of LQR, while allowing for sophisticated stochastic modeling afforded by linear MDPs, without estimating the transition probabilities, thereby enabling direct policy improvement. We use tools from control theory to provide theoretical guarantees on the stability of the system under the learned policy and provide a sample complexity analysis for its convergence to the optimal policy. We illustrate our results via a numerical example that demonstrates the effectiveness of our approach in learning the optimal control policy under partially known stochastic dynamics.

math.OC↗

arXiv2025

Thumb on the Scale: Optimal Loss Weighting in Last Layer Retraining

While machine learning models become more capable in discriminative tasks at scale, their ability to overcome biases introduced by training data has come under increasing scrutiny. Previous results suggest that there are two extremes of parameterization with very different behaviors: the population (underparameterized) setting where loss weighting is optimal and the separable overparameterized setting where loss weighting is ineffective at ensuring equal performance across classes. This work explores the regime of last layer retraining (LLR) in which the unseen limited (retraining) data is frequently inseparable and the model proportionately sized, falling between the two aforementioned extremes. We show, in theory and practice, that loss weighting is still effective in this regime, but that these weights \emph{must} take into account the relative overparameterization of the model.

cs.LG↗

arXiv2025

CORAL: Disentangling Latent Representations in Long-Tailed Diffusion

Diffusion models have achieved impressive performance in generating high-quality and diverse synthetic data. However, their success typically assumes a class-balanced training distribution. In real-world settings, multi-class data often follow a long-tailed distribution, where standard diffusion models struggle -- producing low-diversity and lower-quality samples for tail classes. While this degradation is well-documented, its underlying cause remains poorly understood. In this work, we investigate the behavior of diffusion models trained on long-tailed datasets and identify a key issue: the latent representations (from the bottleneck layer of the U-Net) for tail class subspaces exhibit significant overlap with those of head classes, leading to feature borrowing and poor generation quality. Importantly, we show that this is not merely due to limited data per class, but that the relative class imbalance significantly contributes to this phenomenon. To address this, we propose COntrastive Regularization for Aligning Latents (CORAL), a contrastive latent alignment framework that leverages supervised contrastive losses to encourage well-separated latent class representations. Experiments demonstrate that CORAL significantly improves both the diversity and visual quality of samples generated for tail classes relative to state-of-the-art methods.

cs.LG↗

arXiv2025

GeoClip: Geometry-Aware Clipping for Differentially Private SGD

Differentially private stochastic gradient descent (DP-SGD) is the most widely used method for training machine learning models with provable privacy guarantees. A key challenge in DP-SGD is setting the per-sample gradient clipping threshold, which significantly affects the trade-off between privacy and utility. While recent adaptive methods improve performance by adjusting this threshold during training, they operate in the standard coordinate system and fail to account for correlations across the coordinates of the gradient. We propose GeoClip, a geometry-aware framework that clips and perturbs gradients in a transformed basis aligned with the geometry of the gradient distribution. GeoClip adaptively estimates this transformation using only previously released noisy gradients, incurring no additional privacy cost. We provide convergence guarantees for GeoClip and derive a closed-form solution for the optimal transformation that minimizes the amount of noise added while keeping the probability of gradient clipping under control. Experiments on both tabular and image datasets demonstrate that GeoClip consistently outperforms existing adaptive clipping methods under the same privacy budget.

cs.LG↗

arXiv2025

POCAII: Parameter Optimization with Conscious Allocation using Iterative Intelligence

In this paper we propose for the first time the hyperparameter optimization (HPO) algorithm POCAII. POCAII differs from the Hyperband and Successive Halving literature by explicitly separating the search and evaluation phases and utilizing principled approaches to exploration and exploitation principles during both phases. Such distinction results in a highly flexible scheme for managing a hyperparameter optimization budget by focusing on search (i.e., generating competing configurations) towards the start of the HPO process while increasing the evaluation effort as the HPO comes to an end. POCAII was compared to state of the art approaches SMAC, BOHB and DEHB. Our algorithm shows superior performance in low-budget hyperparameter optimization regimes. Since many practitioners do not have exhaustive resources to assign to HPO, it has wide applications to real-world problems. Moreover, the empirical evidence showed how POCAII demonstrates higher robustness and lower variance in the results. This is again very important when considering realistic scenarios with extremely expensive models to train.

cs.LG↗

arXiv2025

Lower Bounds on the MMSE of Adversarially Inferring Sensitive Features

We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds on the true MMSE of inferring sensitive features from noisy observations of other correlated features. These bounds are expressed in terms of the empirical MMSE under a restricted hypothesis class and a non-negative error term. The error term captures both the estimation error due to finite number of samples and the approximation error from using a restricted hypothesis class. For linear predictive models, we derive closed-form bounds, which are order optimal in terms of the noise variance, on the approximation error for several classes of relationships between the sensitive and non-sensitive features, including linear mappings, binary symmetric channels, and class-conditional multi-variate Gaussian distributions. We also present a new lower bound that relies on the MSE computed on a hold-out validation dataset of the MMSE estimator learned on finite-samples and a restricted hypothesis class. Through empirical evaluation, we demonstrate that our framework serves as an effective tool for MMSE-based adversarial evaluation of sensitive feature inference that balances theoretical guarantees with practical efficiency.

stat.ML↗

arXiv2025

Reveal-or-Obscure: A Differentially Private Sampling Algorithm for Discrete Distributions

We introduce a differentially private (DP) algorithm called reveal-or-obscure (ROO) to generate a single representative sample from a dataset of $n$ observations drawn i.i.d. from an unknown discrete distribution $P$. Unlike methods that add explicit noise to the estimated empirical distribution, ROO achieves $\epsilon$-differential privacy by randomly choosing whether to "reveal" or "obscure" the empirical distribution. While ROO is structurally identical to Algorithm 1 proposed by Cheu and Nayak (arXiv:2412.10512), we prove a strictly better bound on the sampling complexity than that established in Theorem 12 of (arXiv:2412.10512). To further improve the privacy-utility trade-off, we propose a novel generalized sampling algorithm called Data-Specific ROO (DS-ROO), where the probability of obscuring the empirical distribution of the dataset is chosen adaptively. We prove that DS-ROO satisfies $\epsilon$-DP, and provide empirical evidence that DS-ROO can achieve better utility under the same privacy budget of vanilla ROO.

cs.IT↗

arXiv2025

Optimizing Noise Distributions for Differential Privacy

We propose a unified optimization framework for designing continuous and discrete noise distributions that ensure differential privacy (DP) by minimizing R\'enyi DP, a variant of DP, under a cost constraint. R\'enyi DP has the advantage that by considering different values of the R\'enyi parameter $\alpha$, we can tailor our optimization for any number of compositions. To solve the optimization problem, we reduce it to a finite-dimensional convex formulation and perform preconditioned gradient descent. The resulting noise distributions are then compared to their Gaussian and Laplace counterparts. Numerical results demonstrate that our optimized distributions are consistently better, with significant improvements in $(\varepsilon, \delta)$-DP guarantees in the moderate composition regimes, compared to Gaussian and Laplace distributions with the same variance.

cs.IT↗

arXiv2024

Generalized Smooth Stochastic Variational Inequalities: Almost Sure Convergence and Convergence Rates

This paper focuses on solving a stochastic variational inequality (SVI) problem under relaxed smoothness assumption for a class of structured non-monotone operators. The SVI problem has attracted significant interest in the machine learning community due to its immediate application to adversarial training and multi-agent reinforcement learning. In many such applications, the resulting operators do not satisfy the smoothness assumption. To address this issue, we focus on a weaker generalized smoothness assumption called $\alpha$-symmetric. Under $p$-quasi sharpness and $\alpha$-symmetric assumptions on the operator, we study clipped projection (gradient descent-ascent) and clipped Korpelevich (extragradient) methods. For these clipped methods, we provide the first almost-sure convergence results without making any assumptions on the boundedness of either the stochastic operator or the stochastic samples. We also provide the first in-expectation unbiased convergence rate results for these methods under a relaxed smoothness assumption for $\alpha \leq \frac{1}{2}$.

math.OC↗

arXiv2024

Optimizing $(L_0, L_1)$-Smooth Functions by Gradient Methods

We study gradient methods for optimizing $(L_0, L_1)$-smooth functions, a class that generalizes Lipschitz-smooth functions and has gained attention for its relevance in machine learning. We provide new insights into the structure of this function class and develop a principled framework for analyzing optimization methods in this setting. While our convergence rate estimates recover existing results for minimizing the gradient norm in nonconvex problems, our approach significantly improves the best-known complexity bounds for convex objectives. Moreover, we show that the gradient method with Polyak stepsizes and the normalized gradient method achieve nearly the same complexity guarantees as methods that rely on explicit knowledge of~$(L_0, L_1)$. Finally, we demonstrate that a carefully designed accelerated gradient method can be applied to $(L_0, L_1)$-smooth functions, further improving all previous results.

math.OC↗

arXiv2024

Label Noise Robustness for Domain-Agnostic Fair Corrections via Nearest Neighbors Label Spreading

Last-layer retraining methods have emerged as an efficient framework for correcting existing base models. Within this framework, several methods have been proposed to deal with correcting models for subgroup fairness with and without group membership information. Importantly, prior work has demonstrated that many methods are susceptible to noisy labels. To this end, we propose a drop-in correction for label noise in last-layer retraining, and demonstrate that it achieves state-of-the-art worst-group accuracy for a broad range of symmetric label noise and across a wide variety of datasets exhibiting spurious correlations. Our proposed approach uses label spreading on a latent nearest neighbors graph and has minimal computational overhead compared to existing methods.

cs.LG↗

arXiv2024

Theoretical Guarantees of Data Augmented Last Layer Retraining Methods

Ensuring fair predictions across many distinct subpopulations in the training data can be prohibitive for large models. Recently, simple linear last layer retraining strategies, in combination with data augmentation methods such as upweighting, downsampling and mixup, have been shown to achieve state-of-the-art performance for worst-group accuracy, which quantifies accuracy for the least prevalent subpopulation. For linear last layer retraining and the abovementioned augmentations, we present the optimal worst-group accuracy when modeling the distribution of the latent representations (input to the last layer) as Gaussian for each subpopulation. We evaluate and verify our results for both synthetic and large publicly available datasets.

cs.LG↗