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Vijay Gupta

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4 papers

2 author rows

AAAI Conference 2026 Conference Paper

Parameter-free Optimal Rates for Nonlinear Semi-Norm Contractions with Applications to Q-Learning

Ankur Naskar
Gugan Thoppe
Vijay Gupta

Algorithms for solving nonlinear fixed-point equations---such as average-reward Q-learning and TD-learning---often involve semi-norm contractions. Achieving parameter-free optimal convergence rates for these methods via Polyak–Ruppert averaging has remained elusive, largely due to the non-monotonicity of such semi-norms. We close this gap by (i.) recasting the averaged error as a linear recursion involving a nonlinear perturbation, and (ii.) taming the nonlinearity by coupling the semi-norm's contraction with the monotonicity of a suitably induced norm. Our main result yields the first parameter-free ~O(1/√t) optimal rates for Q-learning in both average-reward and exponentially discounted settings, where t denotes the iteration index. The result applies within a broad framework that accommodates both synchronous and asynchronous updates, single-agent and distributed deployments, and data streams obtained from either simulators or along Markovian trajectories.

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ICML Conference 2025 Conference Paper

End-to-End Learning Framework for Solving Non-Markovian Optimal Control

Xiaole Zhang
Peiyu Zhang 0002
Xiongye Xiao
Shixuan Li
Vasileios Tzoumas
Vijay Gupta
Paul Bogdan

Integer-order calculus fails to capture the long-range dependence (LRD) and memory effects found in many complex systems. Fractional calculus addresses these gaps through fractional-order integrals and derivatives, but fractional-order dynamical systems pose substantial challenges in system identification and optimal control tasks. In this paper, we theoretically derive the optimal control via linear quadratic regulator (LQR) for fractional-order linear time-invariant (FOLTI) systems and develop an end-to-end deep learning framework based on this theoretical foundation. Our approach establishes a rigorous mathematical model, derives analytical solutions, and incorporates deep learning to achieve data-driven optimal control of FOLTI systems. Our key contributions include: (i) proposing a novel method for system identification and optimal control strategy in FOLTI systems, (ii) developing the first end-to-end data-driven learning framework, Fractional-Order Learning for Optimal Control (FOLOC), that learns control policies from observed trajectories, and (iii) deriving theoretical bounds on the sample complexity for learning accurate control policies under fractional-order dynamics. Experimental results indicate that our method accurately approximates fractional-order system behaviors without relying on Gaussian noise assumptions, pointing to promising avenues for advanced optimal control.

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NeurIPS Conference 2025 Conference Paper

Principled Long-Tailed Generative Modeling via Diffusion Models

Pranoy Das
Kexin Fu
Abolfazl Hashemi
Vijay Gupta

Deep generative models, particularly diffusion models, have achieved remarkable success but face significant challenges when trained on real-world, long-tailed datasets- where few "head" classes dominate and many "tail" classes are underrepresented. This paper develops a theoretical framework for long-tailed learning via diffusion models through the lens of deep mutual learning. We introduce a novel regularized training objective that combines the standard diffusion loss with a mutual learning term, enabling balanced performance across all class labels, including the underrepresented tails. Our approach to learn via the proposed regularized objective is to formulate it as a multi-player game, with Nash equilibrium serving as the solution concept. We derive a non-asymptotic first-order convergence result for individual gradient descent algorithm to find the Nash equilibrium. We show that the Nash gap of the score network obtained from the algorithm is upper bounded by $\mathcal{O}(\frac{1}{\sqrt{T_{train}}}+\beta)$ where $\beta$ is the regularizing parameter and $T_{train}$ is the number of iterations of the training algorithm. Furthermore, we theoretically establish hyper-parameters for training and sampling algorithm that ensure that we find conditional score networks (under our model) with a worst case sampling error $\mathcal{O}(\epsilon+1), \forall \epsilon>0$ across all class labels. Our results offer insights and guarantees for training diffusion models on imbalanced, long-tailed data, with implications for fairness, privacy, and generalization in real-world generative modeling scenarios.

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NeurIPS Conference 2022 Conference Paper

Revisit last-iterate convergence of mSGD under milder requirement on step size

Ruinan Jin
Xingkang He
Lang Chen
Difei Cheng
Vijay Gupta

Understanding convergence of SGD-based optimization algorithms can help deal with enormous machine learning problems. To ensure last-iterate convergence of SGD and momentum-based SGD (mSGD), the existing studies usually constrain the step size $\epsilon_{n}$ to decay as $\sum_{n=1}^{+\infty}\epsilon_{n}^{2} 0$ by removing the common requirement in the literature on the strong convexity of the loss function. Some experiments are given to illustrate the developed results.

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