arXiv research

New dynamics for SGD in small learning rate regime.

We derive an algorithm that achieves the optimal (within constants) pseudo-regret in both adversarial and stochastic multi-armed bandits without prior knowledge of the regime and time horizon. The algorithm is based on online mirror descent (OMD) with Tsallis entropy regularization with power $α=1/2$ and reduced-varian…

New algorithms reduce regret in online MDPs by adapting to data and variance.

In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modelling framework extends the Heston stochastic volatility model by including the CIR stochastic interest rate and model paramete…

Paper solves complex game theory problems with new equations.

New algorithms minimize regret in both adversarial and stochastic contexts.

The paper solves a complex control problem with stochastic elements and switching conditions.

Study optimal liquidation with multiple regimes using BSDEs with singular terminal values.

Model captures external influences through random parameters and regime switching.

New algorithms reduce regret in both stochastic and adversarial partial monitoring problems.

Solves optimal control for stochastic processes with absorbing states.

Algorithm for bandits with switching costs achieves optimal regret bounds.

Averaged SGD achieves optimal convergence rate for neural networks in the NTK regime.

New findings show mini-batch SGD operates in a 'Edge of Stochastic Stability' regime.

The paper analyzes SGD in high-dimensional networks, revealing new scaling limits.

In this paper, we consider a discrete time economy where we assume that the short term interest rate follows a quadratic term structure of a regime switching asset process. The possible non-linear structure and the fact that the interest rate can have different economic or financial trends justify the interest of Regim…

New algorithm ensures global convergence in deep neural networks beyond NTK regime.

We consider the stochastic linear (multi-armed) contextual bandit problem with the possibility of hidden simple multi-armed bandit structure in which the rewards are independent of the contextual information. Algorithms that are designed solely for one of the regimes are known to be sub-optimal for the alternate regime…

The paper analyzes the stationarity of stochastic Volterra integral equations and introduces fake stationary regimes.

Study indifference pricing for insurance policies in a regime-switching market model.

This paper presents the construction of a particle filter, which incorporates elements inspired by genetic algorithms, in order to achieve accelerated adaptation of the estimated posterior distribution to changes in model parameters. Specifically, the filter is designed for the situation where the subsequent data in on…

Momentum affects optimization differently at small vs large batch sizes near instability.

SGD works well with large learning rates at the edge of stability.

Study the properties of SGD in non-vanishing learning rate regime.

Study optimal liquidation strategies with infinite horizon and regime switching.

Volatility modelling has become a significant area of research within Financial Mathematics. Wiener process driven stochastic volatility models have become popular due their consistency with theoretical arguments and empirical observations. However such models lack the ability to take into account long term and fundame…

Paper derives analytical formulas for NLD-CEV moments with regime switching.

New findings support a new community recovery threshold for Stochastic Block Model with many communities.

We present a new strategy for gap estimation in randomized algorithms for multiarmed bandits and combine it with the EXP3++ algorithm of Seldin and Slivkins (2014). In the stochastic regime the strategy reduces dependence of regret on a time horizon from $(\ln t)^3$ to $(\ln t)^2$ and eliminates an additive factor of o…

Regime switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of regime switching calibration is the Hamilton filter. We propose using the Baum-Welch algorithm, an established technique from Engineering, to calibrate regime switching models instead. …

We study the problem of dynamically trading futures in a regime-switching market. Modeling the underlying asset price as a Markov-modulated diffusion process, we present a utility maximization approach to determine the optimal futures trading strategy. This leads to the analysis of the associated system of Hamilton-Jac…

SGD in DLNs reveals feature learning dynamics.

We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.

Proves convergence of neural networks in a two-timescale regime.

In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead of using two deterministic bounds, the uncertain volatility fluctuates between …

Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with theoreticians pursuing mathematical optimality at a cost of obtaining specialized…

FTPL policy achieves best-of-both-worlds regret in decoupled bandits with reduced computational cost.

Stochastic Gradient Descent phases explained for deep networks.

Stochastic gradient method converges as fast as deterministic for overparametrized models.

This work models market regimes using CTMSTOU and simulates trading policies.

The study extends stochastic block models to geometric settings, focusing on community detection and information flow.

The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.

Random learning rate improves neural network training without extra cost.

The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.

Paper provides tail bounds for stochastic mirror descent in heavy-tailed noise.

We discuss a simple, exactly solvable model of stochastic stock dynamics that incorporates regime switching between healthy and distressed regimes. Using this model, which is analytically tractable, we discuss a way of extracting expected returns for stocks from realized CDS spreads, essentially, the CDS market sentime…

New algorithms improve sampling from complex distributions.

A hybrid approach detects financial market regime switches using PCA and k-means.