We study how to fine-tune LLMs using user-edit deployment data consisting of a set of context, an agent's response, and user edits. This deployment data is naturally generated by users in applications such as LLMs-based writing assistants and coding agents. The natural origin of user edits makes it a desired source for adapting and personalizing of LLMs. In this setup, there emerges a unification of various feedback types namely preferences, supervised labels, and cost that are typically studied separately in the literature. In this paper, we initiate the theoretical investigation of learning from user edits.

Zeroth-order optimization (ZOO) is an important framework for stochastic optimization when gradients are unavailable or expensive to compute. A potential limitation of existing ZOO methods is the bias inherent in most gradient estimators unless the perturbation stepsize vanishes. In this paper, we overcome this biasedness issue by proposing a novel family of unbiased gradient estimators based solely on function evaluations. By reformulating directional derivatives as a telescoping series and sampling from carefully designed distributions, we construct estimators that eliminate bias while maintaining favorable variance. We analyze their theoretical properties, derive optimal scaling distributions and perturbation stepsizes of four specific constructions, and prove that SGD using the proposed estimators achieves optimal complexity for smooth non-convex objectives. Experiments on synthetic tasks and language model fine-tuning confirm the superior accuracy and convergence of our approach compared to standard methods.

Applying Claim 3, we can find a finite setF for which γk RF implies that eachΦkI,j has the property (12).

To that aim we introduce new g-convex optimization results, of independent interest: we show global linear convergence for metric-projected Riemannian gradient descent and improve existing accelerated methods by reducing geometric constants. Additionally, we complete the analysis of two previous works applying to the Riemannian min-max case by removing an assumption about iterates staying in a pre-specified compact set.

With increasing real world applications of machine learning, models are often required to comply with certain domain based requirements, e.g., safety guarantees in aircraft systems, legal constraints in a loan approval model. A natural way to represent these properties is in the form of constraints. Including such constraints in machine learning is typically done by the means of regularization, which does not guarantee satisfaction of the constraints. In this paper, we present a machine learning approach that can handle a wide variety of constraints, and guarantee that these constraints will be satisfied by the model even on unseen data. We cast machine learning as a maximum satisfiability problem, and solve it using a novel algorithm SaDe which combines constraint satisfaction with gradient descent. We demonstrate on three use cases that this approach learns models that provably satisfy the given constraints.

As gradient-free stochastic optimization gains emerging attention for a wide range of applications recently, the demand for uncertainty quantification of parameters obtained from such approaches arises. In this paper, we investigate the problem of statistical inference for model parameters based on gradient-free stochastic optimization methods that use only function values rather than gradients. We first present central limit theorem results for Polyak-Ruppert-averaging type gradient-free estimators. The asymptotic distribution reflects the trade-off between the rate of convergence and function query complexity. We next construct valid confidence intervals for model parameters through the estimation of the covariance matrix in a fully online fashion. We further give a general gradient-free framework for covariance estimation and analyze the role of function query complexity in the convergence rate of the covariance estimator. This provides a one-pass computationally efficient procedure for simultaneously obtaining an estimator of model parameters and conducting statistical inference. Finally, we provide numerical experiments to verify our theoretical results and illustrate some extensions of our method for various machine learning and deep learning applications.

We consider the problem of online learning and its application to solving minimax games. For the online learning problem, Follow the Perturbed Leader (FTPL) is a widely studied algorithm which enjoys the optimal $O(T^{1/2})$ worst-case regret guarantee for both convex and nonconvex losses. In this work, we show that when the sequence of loss functions is predictable, a simple modification of FTPL which incorporates optimism can achieve better regret guarantees, while retaining the optimal worst-case regret guarantee for unpredictable sequences. A key challenge in obtaining these tighter regret bounds is the stochasticity and optimism in the algorithm, which requires different analysis techniques than those commonly used in the analysis of FTPL. The key ingredient we utilize in our analysis is the dual view of perturbation as regularization. While our algorithm has several applications, we consider the specific application of minimax games. For solving smooth convex-concave games, our algorithm only requires access to a linear optimization oracle. For Lipschitz and smooth nonconvex-nonconcave games, our algorithm requires access to an optimization oracle which computes the perturbed best response. In both these settings, our algorithm solves the game up to an accuracy of $O(T^{-1/2})$ using $T$ calls to the optimization oracle. An important feature of our algorithm is that it is highly parallelizable and requires only $O(T^{1/2})$ iterations, with each iteration making $O(T^{1/2})$ parallel calls to the optimization oracle.