arXiv research

Paper proves convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.

Deep learning solves non-Markovian FBSDEs for utility maximization.

Lyapunov-based analysis shows polynomial sample complexity for WCMDPs and RBs.

Unified framework for Brownian motion distances on specific geometric manifolds.

We analyze a market impact game between $n$ risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in t…

We propose a model of inter-bank lending and borrowing which takes into account clearing debt obligations. The evolution of log-monetary reserves of $N$ banks is described by coupled diffusions driven by controls with delay in their drifts. Banks are minimizing their finite-horizon objective functions which take into a…

Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha form, with the exponent alpha=3/2 in case of Hermitian coupling matrices, or slight…

Paper achieves $ε^{-2}$ sample complexity for actor-critic methods with minimal assumptions.

Sharp eigenvalue bounds and splitting for modified Ricci flow.

Motivated by a probabilistic approach to Kahler-Einstein metrics we consider a general non-equilibrium statistical mechanics model in Euclidean space consisting of the stochastic gradient flow of a given (possibly singular) quasi-convex N-particle interaction energy. We show that a deterministic "macroscopic" evolution…

SGLD proves geometric ergodicity via reflection coupling for nonconvex log-concave distributions.

DRIFT uses RL to automate functional software testing efficiently.

Classifying streaming data requires the development of methods which are computationally efficient and able to cope with changes in the underlying distribution of the stream, a phenomenon known in the literature as concept drift. We propose a new method for detecting concept drift which uses an Exponentially Weighted M…

We provide a verification and characterization result of optimal maximal sub-solutions of BSDEs in terms of fully coupled forward backward stochastic differential equations. We illustrate the application thereof in utility optimization with random endowment under probability and discounting uncertainty. We show with ex…

Paper proposes a weak approximation of reflection coupling for non-convex optimization.

Paper proposes a framework to detect adversarial concept drifts under poisoning attacks.

This paper analyzes microstructure dynamics in coupled markets using CFMMs.

New solutions found for elliptic systems with mixed couplings.

DDG-DA predicts future data distribution to adapt models for predictable concept drift.

KOMET identifies Koopman operators from model parameter trajectories to adapt to evolving data distributions.

Augmented bridge matching preserves coupling information between distributions.

Uniform bounds derived for fully non-linear equations.

Amazon SageMaker Model Monitor detects drift in deployed ML models.

A novel bootstrap method improves concept drift detection in predictive models.

This paper identifies drift Lipschitz budget K as key to diffusion policy expressivity and statistical trade-offs.

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various ki…

This paper analyzes how multiple investors can exploit relative arbitrage opportunities.

Geometric formalism views optimization algorithms as discrete connections, revealing their algebraic curvature and flatness properties.

Transferring knowledge across many streaming processes remains an uncharted territory in the existing literature and features unique characteristics: no labelled instance of the target domain, covariate shift of source and target domain, different period of drifts in the source and target domains. Autonomous transfer l…

Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-asymptotic analysis in the $L^2$ Wasserstein distance of sampling algorithms based on Euler discretisations of SDEs has been recently develop…

Develops an algorithm for bilevel optimization with coupled constraints.

Adaptive financial dataflow system improves model robustness in dynamic markets.

A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choic…

D2SRM solves complex PDEs using deep learning.

Federated Averaging (FedAvg) has emerged as the algorithm of choice for federated learning due to its simplicity and low communication cost. However, in spite of recent research efforts, its performance is not fully understood. We obtain tight convergence rates for FedAvg and prove that it suffers from `client-drift' w…

In this work, we leverage advances in sparse coding techniques to reduce the number of trainable parameters in a fully connected neural network. While most of the works in literature impose $\ell_1$ regularization, DropOut or DropConnect techniques to induce sparsity, our scheme considers feature importance as a criter…

A new method for conditional sampling using paired Wasserstein Autoencoders.

Convolutional Neural Networks (CNNs) have become indispensable for solving machine learning tasks in speech recognition, computer vision, and other areas that involve high-dimensional data. A CNN filters the input feature using a network containing spatial convolution operators with compactly supported stencils. In pra…

Unified theory for optimal execution through signal-adaptive quotes in limit order books.

In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model with default contagion in a large interconnected banking system. Using the metho…

We analyse the optimal exercise of an executive stock option (ESO) written on a stock whose drift parameter falls to a lower value at a change point, an exponentially distributed random time independent of the Brownian motion driving the stock. Two agents, who do not trade the stock, have differing information on the c…

This paper shows how learning the phase-amplitude coupling improves bio-signal classification.

This paper provides guarantees for DFM models using KL divergence.

Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of classic regression solvers. We show that SGD schemes efficiently track the true s…

Deep Reinforcement Learning (RL) recently emerged as one of the most competitive approaches for learning in sequential decision making problems with fully observable environments, e.g., computer Go. However, very little work has been done in deep RL to handle partially observable environments. We propose a new architec…

We consider a banking network represented by a system of stochastic differential equations coupled by their drift. We assume a core-periphery structure, and that the banks in the core hold a bubbly asset. The banks in the periphery have not direct access to the bubble, but can take initially advantage from its increase…

Improved growth strategies by incorporating stochastic factors in asset returns.

A new method for non-rigid point set registration reduces computational complexity.