arXiv research

Characterizes problems solvable via linear convergence algorithms.

Paper solves stochastic contextual linear bandits using linear bandit algorithms.

New method solves linear inverse problems using diffusion models.

The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including con…

Solves a challenging case of Nijenhuis operator linearization in 2D.

Paper proposes a new activation function to reduce overfitting and large weight update issues.

Optimal algorithm for identifying best arm in stochastic linear bandits with fixed confidence.

New classifier combines locally linear kernels for fast and accurate non-linear classification.

MCGDiff uses SGM to guide SMC for solving ill-posed linear inverse problems.

Real-world problems of operations research are typically high-dimensional and combinatorial. Linear programs are generally used to formulate and efficiently solve these large decision problems. However, in multi-period decision problems, we must often compute expected downstream values corresponding to current decision…

Efficient algorithms speed up adversarial training for linear models.

Study Loday algebroids, prove splitting theorem, and linearize problems.

Graph neural networks improve solving linear optimization problems.

Unified approach for optimizing predictions in linear programming and inverse problems.

We reformulate LIPs as min-max problems for easier solution.

We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample corresponds to which model) are not observed. We give a tractable a…

Paper uses SGD for solving linear inverse problems, improving empirical performance.

Efficiently solves inverse PDE problems with Gaussian processes.

A new algorithm improves stochastic linear bandit performance using residual bootstrap.

AM converges super-linearly for solving mixed linear regression problems.

New method for estimating parameters in inverse problems using double robustness.

The paper tightens the regret rate for linear bandit problems.

New method distinguishes feature relevance in non-linear contexts.

In this article we dwell into the class of so called ill posed Linear Inverse Problems (LIP) in machine learning, which has become almost a classic in recent times. The fundamental task in an LIP is to recover the entire signal / data from its relatively few random linear measurements. Such problems arise in variety of…

Physics-informed GP regression solves eigenvalue problems by identifying non-trivial eigenspaces.

Two algorithms solve nonconvex minimax problems with linear constraints, achieving complexity guarantees.

We consider optimal investment problems for a diffusion market model with non-observable random drifts that evolve as an Ito's process. Admissible strategies do not use direct observations of the market parameters, but rather use historical stock prices. For a non-linear problem with a general performance criterion, th…

We show that fundamental learning tasks, such as finding an approximate linear separator or linear regression, require memory at least \emph{quadratic} in the dimension, in a natural streaming setting. This implies that such problems cannot be solved (at least in this setting) by scalable memory-efficient streaming alg…

Characterizes kernel of linearization for minimal surfaces problem

Algorithm solves word problem in mapping class group quickly.

Study solves inverse problems for equations with fractional nonlinearities.

New algorithms tackle RKHS bandits with reduced complexity and improved performance.

The paper analyzes the sample complexities for policy evaluation with linear function approximation.

DART optimizes subset selection in non-linear bandit problems.

GD outperforms ridge regression and SGD in linear regression problems.

Financial portfolios are often optimized for maximum profit while subject to a constraint formulated in terms of the Conditional Value-at-Risk (CVaR). This amounts to solving a linear problem. However, in its original formulation this linear problem has a very large number of linear constraints, too many to be enforced…

Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging problem lacking an analytical solution. We derive a new expectation maximization …

Study non-linear combinatorial bandits with polynomial rewards, finding significant differences from linear cases.

Paper models non-linear dynamics from time series data.

The paper examines scalar fourth-order linear differential operators and their invariants.

New algorithms improve linear bandit performance with low computation.

We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.

Efficiently extracts linear dynamics from complex observations.

This paper studies the addition of linear constraints to the Support Vector Regression (SVR) when the kernel is linear. Adding those constraints into the problem allows to add prior knowledge on the estimator obtained, such as finding probability vector or monotone data. We propose a generalization of the Sequential Mi…

In this article we study the linearized anisotropic Calderon problem. In a compact manifold with boundary, this problem amounts to showing that products of harmonic functions form a complete set. Assuming that the manifold is transversally anisotropic, we show that the boundary measurements determine an FBI type transf…

Solves Dirichlet problem for elliptic equations on Hermitian manifolds.

Paper studies Gaussian approximation in linear regression with rates derived.

Solves the invariant linearization problem for Lie groupoids.