A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We give nearly matching upper and lower bounds on the oracle complexity of finding ε-stationary points (∥∇F(x)∥≤ε) in stochastic convex optimization. We jointly analyze the oracle complexity in both the local stochastic oracle model and the global oracle (or, statistical learning) model. This allows u…
We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds for several specific parallel optimization settings, including delayed …
Paper proposes a new method to stabilize noisy gradient algorithms.
problem Stochastic-gradient Langevin algorithms can introduce bias when taming denominators depend on stochastic-gradient realizations.
method Proposes a structure-preserving framework for designing tamed denominators that avoid unnecessary taming and maintain the stabilizing effect of taming.
result The method avoids stationary bias and explains the stationary error split into bias and remaining error.
We study the computational tractability of PAC reinforcement learning with rich observations. We present new provably sample-efficient algorithms for environments with deterministic hidden state dynamics and stochastic rich observations. These methods operate in an oracle model of computation -- accessing policy and va…
We present a generic framework for trading off fidelity and cost in computing stochastic gradients when the costs of acquiring stochastic gradients of different quality are not known a priori. We consider a mini-batch oracle that distributes a limited query budget over a number of stochastic gradients and aggregates th…
Paper addresses online alignment of large language models under uncertain preference feedback.
problem Online alignment of large language models with misspecified preference feedback.
method Formulates an oracle-robust objective as a worst-case optimization problem for log-linear policies, and develops projected stochastic composite updates.
result Shows that the robust objective admits an exact closed-form decomposition and achieves O(ε−2) oracle complexity.
Study how noisy labels affect semi-supervised learning.
problem Effect of noisy labels on semi-supervised learning performance.
method Proposed an algorithm derived from a continuous relaxation of the Maximum A Posteriori (MAP) estimator for a Degree Corrected Stochastic Block Model (DC-SBM).
result Our approach achieves promising performance even with very noisy labeled data.
Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and statistics, gaining an understanding of these complexity-theoretic issues is importa…
SARAH and SPIDER are two recently developed stochastic variance-reduced algorithms, and SPIDER has been shown to achieve a near-optimal first-order oracle complexity in smooth nonconvex optimization. However, SPIDER uses an accuracy-dependent stepsize that slows down the convergence in practice, and cannot handle objec…
We present a probabilistic modeling framework and adaptive sampling algorithm wherein unsupervised generative models are combined with black box predictive models to tackle the problem of input design. In input design, one is given one or more stochastic "oracle" predictive functions, each of which maps from the input …
In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate O(ε21) improving over the projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan an…
In this paper, we initiate a rigorous theoretical study of clustering with noisy queries (or a faulty oracle). Given a set of n elements, our goal is to recover the true clustering by asking minimum number of pairwise queries to an oracle. Oracle can answer queries of the form : "do elements u and v belong to the…
Probabilistic Bisection Algorithm performs root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and location-dependent, so that model inference and Bayesian knowledge updating must be performed s…
We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly non-differentiable but convex component. We propose a proximal stochastic gradie…