arXiv research

Quantum computing improves feature selection in machine learning.

Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.

Eigen-decomposition simplifies quadratic programming with equality constraints.

Paper proposes a QUBO formulation that reduces binary variables in Bayesian network learning.

Improved VQE for large DPO problems in finance.

Integrates prediction models into portfolio optimization for better asset allocation.

Simulated Bifurcation outperforms quantum machines in community detection.

Quantum algorithm improves sparse vector recovery from noisy measurements.

Investigates portfolio optimization with and without gearing constraints.

Study uses RL to optimize investment with financial constraints, showing exploration benefits.

Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most popular, quasi-Newto…

In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem by regularizing the rank function with Huber loss. Huber loss is leveraged to c…

New approach reduces unconstrained linear bandits to simpler optimization problems.

Develops parameter-free online mirror descent for optimal dynamic regret.

A new optimization algorithm improves convergence in unconstrained problems.

Quantum computers can optimize foreign exchange reserves management.

New approach to sparse optimal transport for matching tokens with experts.

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACV…

Optimizes train schedules and maintenance using CP and QA.

Our paper explains deep neural collapse in multiple layers.

Paper proposes distributed optimization for federated learning with theoretical guarantees.

We clarify what fairness guarantees we can and cannot expect to follow from unconstrained machine learning. Specifically, we characterize when unconstrained learning on its own implies group calibration, that is, the outcome variable is conditionally independent of group membership given the score. We show that under r…

Second-order methods improve differential privacy in convex optimization.

We propose an online convex optimization algorithm (RescaledExp) that achieves optimal regret in the unconstrained setting without prior knowledge of any bounds on the loss functions. We prove a lower bound showing an exponential separation between the regret of existing algorithms that require a known bound on the los…

A new L-BFGS method tackles large-scale optimization with fewer evaluations.

Solves VaR-constrained portfolio optimization in markets with stochastic volatility.

VAV method optimizes learning rate for faster, stable SGD convergence.

Quantum computing speeds up linear regression training.

Unconstrained MLIPs outperform constrained ones in accuracy and speed.

Study optimal portfolio management with periodic evaluations in stochastic models, considering convex constraints.

The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: Trading strategies must take values in a (possibly random and time-de…

We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the predictions of the optimal comparator are invariant under any linear transformation of th…

New algorithm minimizes cumulative loss in dynamic linear bandits without prior knowledge of comparator switches.

New methods solve complex optimization problems in machine learning.

A key problem in financial mathematics is the forecasting of financial crashes: if we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem. Financial crashes are inherently difficult to predict, even for a regulator whic…

A new reinforcement learning method improves Max-Cut solutions without needing training data.

One-pass SGD dynamics in overparameterized quadratic networks show slow escape from poor solutions.

Paper proves fair classification can be done via simple thresholding.

In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination where the risk is measured by a distortion risk measure and the premium is given by a distortion premium principle. Firstly, we show that how optimal reinsurance mod…

Quantum machine learning: Adiabatic quantum SVM outperforms classical methods.

Paper analyzes regret bounds for unconstrained online optimization.

Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a lower-dimensional problem. Such dimensionality reduction is essential in computation-limite…

Proposes a quantum-inspired algorithm for selecting representative data subsets.

Quantum algorithm finds extrema in discrete optimisation problems.

Quantum machine learns to clean up blurry images.

Neural networks have been used prominently in several machine learning and statistics applications. In general, the underlying optimization of neural networks is non-convex which makes their performance analysis challenging. In this paper, we take a novel approach to this problem by asking whether one can constrain neu…

The natural gradient of ELBO vanishes in unconstrained optimization, simplifying learning.

This article presents a new methodology called deep Theory of Functional Connections (TFC) that estimates the solutions of partial differential equations (PDEs) by combining neural networks with TFC. TFC is used to transform PDEs with boundary conditions into unconstrained optimization problems by embedding the boundar…