Related papers: Implicit Bias of Mirror Flow on Separable Data
We provide a detailed study on the implicit bias of gradient descent when optimizing loss functions with strictly monotone tails, such as the logistic loss, over separable datasets. We look at two basic questions: (a) what are the…
We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…
We investigate Stochastic Mirror Descent (SMD) with matrix parameters and vector-valued predictions, a framework relevant to multi-class classification and matrix completion problems. Focusing on the overparameterized regime, where the…
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…
We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the…
A new loss function is proposed for neural networks on classification tasks which extends the hinge loss by assigning gradients to its critical points. We will show that for a linear classifier on linearly separable data with fixed step…
In this paper, we propose a continuous-time primal-dual approach for linearly constrained multiobjective optimization problems. A novel dynamical model, called accelerated multiobjective primal-dual flow, is presented with a second-order…
The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic…
Graph models, like other machine learning models, have implicit and explicit biases built-in, which often impact performance in nontrivial ways. The model's faithfulness is often measured by comparing the newly generated graph against the…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
A strongly polynomial algorithm is developed for finding an integer-valued feasible $st$-flow of given flow-amount which is decreasingly minimal on a specified subset $F$ of edges in the sense that the largest flow-value on $F$ is as small…
Mirror Descent is a popular algorithm, that extends Gradients Descent (GD) beyond the Euclidean geometry. One of its benefits is to enable strong convergence guarantees through smooth-like analyses, even for objectives with exploding or…
Motivated by applications in conditional sampling, given a probability measure $\mu$ and a diffeomorphism $\phi$, we consider the problem of simultaneously approximating $\phi$ and the pushforward $\phi_{\#}\mu$ by means of the flow of a…
We establish a connection between the stability of mirror descent and the information ratio by Russo and Van Roy [2014]. Our analysis shows that mirror descent with suitable loss estimators and exploratory distributions enjoys the same…
We study the global convergence of a Fisher-Rao policy gradient flow for infinite-horizon entropy-regularised Markov decision processes with Polish state and action space. The flow is a continuous-time analogue of a policy mirror descent…
We propose a new first-order optimisation algorithm to solve high-dimensional non-smooth composite minimisation problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a…
We analyse a version of the policy iteration algorithm for the discounted infinite-horizon problem for controlled multidimensional diffusion processes, where both the drift and the diffusion coefficient can be controlled. We prove that,…
Exploration is critical for solving real-world decision-making problems such as scientific discovery, where the objective is to generate truly novel designs rather than mimic existing data distributions. In this work, we address the…
We study a continuous-time dynamical system which arises as the limit of a broad class of nonlinearly preconditioned gradient methods. Under mild assumptions, we establish existence of global solutions and derive Lyapunov-based convergence…
We consider online allocation problems with concave revenue functions and resource constraints, which are central problems in revenue management and online advertising. In these settings, requests arrive sequentially during a finite horizon…