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版本更新 · v2arXiv:2602.20457

Oracle-Robust Online Alignment for Large Language Models

Zimeng Li, Mudit Gaur, Vaneet Aggarwal

原文摘要

We study online alignment of large language models under misspecified preference feedback, where the observed preference oracle deviates from an ideal but unknown ground-truth oracle. The online LLM alignment problem is a bi-level reinforcement problem due to the coupling between data collection and policy updates. Recently, the problem has been reduced to a tractable single-level objective in the SAIL (Self-Improving Efficient Online Alignment) framework. In this paper, we introduce a pointwise oracle uncertainty set in this problem and formulate an oracle-robust online alignment objective as a worst-case optimization problem. For log-linear policies, we show that this robust objective admits an exact closed-form decomposition into the original loss function plus an explicit sensitivity penalty. In the finite-response log-linear setting, we develop projected stochastic composite updates for the resulting weakly convex objective and prove $\widetilde{O}(\varepsilon^{-2})$ oracle complexity for reaching approximate stationarity.

cs.LG · stat.ML

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.01562

Finite-Time Online Sample Complexity for Conditional Diffusion Models

Mudit Gaur, Prashant Trivedi, Sasidhar Kunapuli, Amrit Singh Bedi, Vaneet Aggarwal

原文摘要

We study the finite-time training and sampling error of conditional diffusion models trained by online stochastic-gradient denoising score matching. Rather than assuming access to an exact empirical or population risk minimizer, we analyze the score network produced after a finite number of stochastic-gradient updates under an explicit localized Polyak--Łojasiewicz (PL) condition, stochastic-gradient regularity, and a trajectory-containment assumption. Our analysis separates the network approximation complexity from the online training-sample budget and propagates both errors through the reverse diffusion process. Under anisotropic smoothness, a joint intrinsic-dimensional structure for the data and conditioning variables, sub-exponential tails, and explicit approximation-class compatibility, we obtain a conditional score approximation error of order \[ \widetilde{\mathcal O}\!\left(M^{-η_{\mathrm{app}}}\right), \qquad η_{\mathrm{app}} = \frac{2α_x} {2α_x+d_x'+(α_x/α_y)d_y'}, \] where \(M\) denotes the approximation complexity, \(d_x'\) and \(d_y'\) are the intrinsic response and conditioning dimensions, and \(α_x,α_y\) are their corresponding smoothness exponents. For \(N=RB\) online denoising samples used by SGD, the finite-time optimization error is controlled explicitly in terms of the PL, smoothness, gradient-noise, and initialization constants. Combining these ingredients with reverse-process stability yields a total-variation bound that decomposes into terminal-initialization, time-discretization, approximation/localization, and finite-time optimization errors.

cs.LG · cs.AI

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.01559

Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching

Mudit Gaur, Prashant Trivedi, Shuchin Aeron, Amrit Singh Bedi, George K. Atia, Vaneet Aggarwal

原文摘要

Flow matching has emerged as a promising alternative to diffusion-based generative modeling, offering a continuous-time ordinary differential equation formulation with fast sampling and a simple regression-based training objective. Despite its empirical success, some theoretical analyses idealize the learning procedure by assuming that the velocity field is obtained by exact empirical risk minimization. This assumption does not reflect the practical finite-dataset setting, where the empirical flow-matching loss is only approximately minimized by a finite number of stochastic-gradient updates. We develop an empirical-risk-minimizer-free analysis for flow matching that explicitly accounts for both finite-sample statistical error and finite-time empirical optimization error. Our analysis considers a finite dataset of \(N\) flow-matching samples and a learned parameter \(θ_T\) obtained after \(T\) stochastic gradient updates on the empirical objective. Under regularity assumptions on the interpolation path, sub-exponential source and target distributions, approximation by a bounded-parameter smooth neural velocity class, empirical-loss optimization, and uniform flow stability, we prove a guarantee that holds with high probability over the finite training dataset and in expectation over the stochastic-gradient randomness. The resulting bound separates approximation error, statistical error from the finite dataset, tail error from unbounded source and target distributions, and empirical optimization error from approximate minimization of the finite-sample objective.

cs.LG · cs.AI

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.01500

Improved Sample Complexity Analysis For First Order Bilevel Reinforcement Learning

Mudit Gaur, Naman Saxena, Vaneet Aggarwal

原文摘要

Bilevel reinforcement learning optimizes an upper-level objective through the policy response to a lower-level reinforcement learning problem. Such problems arise when learning a reward model while adapting a policy to that reward. However, a gap remains between sample-complexity guarantees and practical actor--critic training. Tabular analyses restrict applicability to finite spaces, while continuous-state analyses often impose a uniform Polyak--Łojasiewicz (PL) condition. We show that this condition need not hold even for smooth positive policies with exactly representable values. We develop a single-loop, fully first-order method for continuous states and finite actions with specified multilayer neural actors and a persistently trained nonlinear critic built from fixed features. Under explicit initialization, regularity, feature-excitation, and value-realizability conditions, fixed reference-KL regularization yields local curvature, and we prove containment of the coupled iterates. Shared trajectories control sampling noise, while paired critic analysis controls normalized critic-error differences as the response perturbation shrinks. A joint descent and tracking argument establishes an improved $\widetilde{\mathcal O}(\varepsilon^{-2})$ sample complexity for $O(\varepsilon)$ expected squared gradient norm of the upper objective induced by the selected regularized policy response, including critic training.

cs.LG · cs.AI

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arXiv ↗PDF ↗