Generalized Distributional Alignment Games for Unbiased Answer-Level Fine-Tuning

• URL: http://arxiv.org/abs/2605.02435v1
• Date: Mon, 04 May 2026 10:34:42 GMT
• Title: Generalized Distributional Alignment Games for Unbiased Answer-Level Fine-Tuning
• Abstract summary: Distributional Alignment Game framework provides powerful variational perspective on Answer-Level Fine-Tuning (ALFT)<n>Standard algorithms for these games rely on estimating logarithmic rewards from small batches, introducing a systematic bias due to Jensen's inequality that can destabilize training.<n>We generalize the alignment game to arbitrary Bregman divergences, showing that for a family of geometries inducing rewards, we can construct provably exact and unbiased estimators.
• Score: 49.24876001249647
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Distributional Alignment Game framework provides a powerful variational perspective on Answer-Level Fine-Tuning (ALFT). However, standard algorithms for these games rely on estimating logarithmic rewards from small batches, introducing a systematic bias due to Jensen's inequality that can destabilize training. In this paper, we systematically resolve this structural estimation bias. First, we generalize the alignment game to arbitrary Bregman divergences, showing that for a family of geometries inducing polynomial rewards, we can construct provably exact and unbiased estimators using U-statistics. Second, for the canonical KL divergence game where an exact solution is impossible, we derive a globally robust minimax polynomial estimator that is provably optimal, achieving the fundamental statistical error limit of $Θ(1/K^2)$, which we establish via the Ditzian-Totik theorem. Finally, we synthesize these two approaches to propose a novel Variance-Optimal Augmented Polynomial Optimization Program (AQP) Estimator, proving that by systematically reducing variance, our method achieves not only optimal bias but also provably accelerated game convergence, leading to more efficient and stable training with zero online computational overhead.

Related papers

• Revisiting Zeroth-Order Hessian Approximation: A Single-Step Policy Optimization Lens [18.253856190297405]
  ZoVH is a suite of variance-reduced estimators for the full Hessian matrix, its regularized inverse, and the bias-corrected inverse Hessian-gradient product.<n>We show that ZoVH achieves superior estimation accuracy and convergence performance in real-world applications.
  arXiv  Detail & Related papers  (2026-05-29T07:55:57Z)
• Provably Adaptive Linear Approximation for the Shapley Value and Beyond [73.0940890296463]
  A fundamental and long-standing challenge is their efficient approximation.<n>We develop a linear-space algorithm that requires $P(|hatboldsymbol-boldsymbol|_2geq)leq $ for all commonly used semi-values.<n>Our algorithm allows explicit minimization of the mean square error for each specific utility function.
  arXiv  Detail & Related papers  (2026-04-09T16:38:14Z)
• Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions [3.6997773420183866]
  We develop new variance-reduction techniques for the forward-reflected-backward splitting (FRBS) method.<n>Unlike unbiased estimators such as mini-batching, developing biased variants faces a fundamental technical challenge.<n>We show that the best oracle complexities for the $n$-finite-sum and expectation settings are $mathcalO(n2/3-2)$ and $mathcalO(-10/3)$, respectively, when employing loopless-SVRG or SAGA.
  arXiv  Detail & Related papers  (2026-03-16T17:39:25Z)
• Unregularized Linear Convergence in Zero-Sum Game from Preference Feedback [50.89125374999765]
  We provide the first convergence guarantee for Optimistic Multiplicative Weights Update ($mathtOMWU$) in NLHF.<n>Our analysis identifies a novel marginal convergence behavior, where the probability of rarely played actions grows exponentially from exponentially small values.
  arXiv  Detail & Related papers  (2025-12-31T12:08:29Z)
• On the Optimal Construction of Unbiased Gradient Estimators for Zeroth-Order Optimization [57.179679246370114]
  A potential limitation of existing methods is the bias inherent in most perturbation estimators unless a stepsize is proposed.<n>We propose a novel family of unbiased gradient scaling estimators that eliminate bias while maintaining favorable construction.
  arXiv  Detail & Related papers  (2025-10-22T18:25:43Z)
• Distributed Sparse Regression via Penalization [5.990069843501885]
  We study linear regression over a network of agents, modeled as an undirected graph (with no centralized node) The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic penalty of the consensus constraint. We show that the proximal-gradient algorithm applied to the penalized problem converges linearly up to a tolerance of the order of the centralized statistical error.
  arXiv  Detail & Related papers  (2021-11-12T01:51:50Z)
• Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Applications [25.410110072480187]
  Wasserstein distances are sensitive to outliers in the considered distributions. We propose a new outlier-robust Wasserstein distance $mathsfW_pvarepsilon$ which allows for $varepsilon$ outlier mass to be removed from each contaminated distribution.
  arXiv  Detail & Related papers  (2021-11-02T04:05:45Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• Distributed Averaging Methods for Randomized Second Order Optimization [54.51566432934556]
  We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization that employ sampling and sketching of the Hessian. We also extend the framework of second order averaging methods to introduce an unbiased distributed optimization framework for heterogeneous computing systems.
  arXiv  Detail & Related papers  (2020-02-16T09:01:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.