Paper proposes a new method to stabilize noisy gradient algorithms.
problem Stochastic-gradient Langevin algorithms can introduce bias when taming denominators depend on stochastic-gradient realizations.
method Proposes a structure-preserving framework for designing tamed denominators that avoid unnecessary taming and maintain the stabilizing effect of taming.
result The method avoids stationary bias and explains the stationary error split into bias and remaining error.
This paper investigates a type of instability that is linked to the greedy policy improvement in approximated reinforcement learning. We show empirically that non-deterministic policy improvement can stabilize methods like LSPI by controlling the improvements' stochasticity. Additionally we show that a suitable represe…
Designing deterministic denominators for SGLD stabilizes large drifts.
problem Stabilizing large drifts in SGLD
method Using state-dependent envelopes and empirical quantiles for activation thresholds
result Proxy-quantile denominators are close to oracle-score behavior and improve deterministic taming choices
Paper explores stability, regularization, and gradient flows for stochastic inverse problems.
problem Recovering random probability distributions from measurements.
method Direct inversion, variational formulation with regularization, and optimization via gradient flows.
result The choice of metric impacts stability and properties of the optimizer.
Unified framework for solving fixed-point equations in deterministic and stochastic settings.
problem Solving fixed-point equations for seminorm-contractive operators in both deterministic and stochastic contexts.
method Fixed-point theorem and stochastic approximation analysis.
result Unified finite-sample bounds for various reinforcement learning algorithms.
Unified treatment of RC in stochastic and deterministic settings.
problem Understanding and generalizing reservoir computing in both deterministic and stochastic contexts.
method Investigation of state-space systems, analysis of fading memory and solution stability, introduction of stochastic echo states.
result Generality of fading memory and solution stability in state-space systems, even without the echo state property.
This paper analyzes how periodic and soft target updates stabilize linear Q-learning.
problem Theoretical explanation of stabilization mechanisms for linear Q-learning.
method Exact analysis using switched linear system dynamics and the joint spectral radius.
result Periodic and soft target updates can guarantee convergence to the exact projected Q-Bellman solution under specific conditions.
Develops a deterministic method to approximate NSDEs for better uncertainty quantification.
problem Computational infeasibility of obtaining well-calibrated uncertainty from NSDEs.
method Bidimensional moment matching algorithm for approximating NSDE transition kernel.
result Deterministic approximation improves uncertainty calibration and prediction accuracy.
Bayesian explanations are more resilient to adversarial attacks than deterministic ones.
problem Stability of saliency-based explanations under adversarial attacks in Neural Networks.
method Empirical and theoretical analysis of Bayesian vs deterministic Neural Networks.
result Bayesian explanations are more stable under adversarial perturbations and direct attacks.
Develops DPG methods for continuous-time RL with deterministic policies.
problem High variance and slow convergence in stochastic policy RL methods.
method Derives continuous-time policy gradient formula and proposes CT-DDPG algorithm.
result CT-DDPG achieves superior stability and faster convergence in continuous-time RL.
Systemic risk measures are crucial for the stability of financial markets, yet classical formulations fail to capture the complexity of market volatility. We propose a new framework for systemic risk measurement on the variable-exponent Bochner-Lebesgue space Lp(⋅), where the exponent p(⋅) is a random va…
SGD works well with large learning rates at the edge of stability.
problem Stochasticity at the edge of stability in deep learning.
method Sharp convergence guarantees for SGD with multiclass cross-entropy loss.
result SGD self-stabilizes, ensuring convergence with large learning rates.
This paper investigates trajectory tracking problem for a class of underactuated autonomous underwater vehicles (AUVs) with unknown dynamics and constrained inputs. Different from existing policy gradient methods which employ single actor-critic but cannot realize satisfactory tracking control accuracy and stable learn…
We propose a heterogeneous agent market model (HAM) in continuous time. The market is populated by fundamental traders and chartists, who both use simple linear trading rules. Most of the related literature explores stability, price dynamics and profitability either within deterministic models or by simulation. Our nov…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a prob…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a prob…
Develops a new reinforcement learning framework for complex control problems.
problem Continuous-time extended mean field control with deterministic policies.
method Model-free sensitivity formula, deterministic policy gradient, local value and advantage-rate representations.
result Demonstrates efficiency, stability, and robustness in solving complex control problems.
Local Interpretable Model-Agnostic Explanations (LIME) is a popular technique used to increase the interpretability and explainability of black box Machine Learning (ML) algorithms. LIME typically generates an explanation for a single prediction by any ML model by learning a simpler interpretable model (e.g. linear cla…
Proposes a new policy gradient algorithm to improve reinforcement learning efficiency and stability.
problem Inefficiency and instability of DDPG in practical applications, and difficulty in controlling Q estimation bias and variance.
method Introduces a Regularly Updated Deterministic (RUD) policy gradient algorithm.
result The RUD algorithm makes better use of new data and has lower Q value variance, leading to improved performance.
Unified kernel framework extends to stochastic systems, improving numerical stability.
problem Extending kernel methods to stochastic dynamical systems with diffusion.
method Unified kernel framework, Feynman-Kac path-integral representations, collocation-based computational framework.
result Kernel equivalence under uniform ellipticity assumptions and improved numerical stability with moderate diffusion.
Clustering is a crucial component of many data mining systems involving the analysis and exploration of various data. Data diversity calls for clustering algorithms to be accurate while providing stable (i.e., deterministic and robust) results on arbitrary input networks. Moreover, modern systems often operate with lar…
Framework simulates market microstructure with stable Hawkes processes.
problem Reproduce realistic market order flow dynamics.
method Deterministic C++ LOB simulator with Hawkes-driven stochastic order flow.
result Derives stability and ergodicity proofs for Hawkes models.
Develops pathwise analysis for log-optimal portfolios using rough paths theory.
problem Analyzing stability and approximation of log-optimal portfolios.
method Pathwise approach based on càdlàg rough paths theory.
result Establishes pathwise stability and error estimates for log-optimal portfolios.
ZDPG learns model-free policies without critics, improving on PG.
problem Model-free policy learning in complex dynamic problems.
method Approximates policy-reward gradients via two-point stochastic evaluations of the Q-function.
result Restores true model-free policy learning without critics, with improved stability and efficiency.
Model predicts alternating market dominance for two competing firms.
problem Alternating market dominance of two competing firms in a competitive market.
method Deterministic model with investment strategy, stability analysis of fixed points, bifurcation diagrams, time-series analysis.
result Leapfrogging regime is stabilized by specific parameter values and high elasticity coefficient.
Continuous control imitation learning fails if expert actions are smooth.
problem Continuous control imitation learning fails if expert actions are smooth.
method Study of imitation learning in discrete-time, continuous state-and-action control systems.
result Any smooth, deterministic imitator policy suffers exponentially larger error than the expert.
New approach to concentration inequalities for unbounded state space dynamical systems.
problem Concentration inequalities for unbounded state space dynamical systems.
method Functional analytic framework, transport-entropy inequality.
result Exponential concentration inequalities for sampling from stationary distribution.
This study analyzes convergence and stability of reinforcement learning algorithms.
problem Understanding the conditions under which reinforcement learning algorithms converge and remain stable.
method Theoretical analysis of convergence and stability of Episodic Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning, and Online Decision Transformers.
result The algorithms can achieve near-optimal behavior if the transition kernel is close to a deterministic kernel.
We provide existence, uniqueness and stability results for affine stochastic Volterra equations with L1-kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance. The strategy we adopt for the existence part is b…
Econometrics is based on the nonempiric notion of utility. Prices, dynamics, and market equilibria are supposed to be derived from utility. Utility is usually treated by economists as a price potential, other times utility rates are treated as Lagrangians. Assumptions of integrability of Lagrangians and dynamics are im…
The paper analyzes the stationarity of stochastic Volterra integral equations and introduces fake stationary regimes.
problem Analyzing the stationarity of non-Markovian dynamical systems described by SVIEs.
method Investigates the properties of SVIE solutions, focusing on stationarity over finite and long time horizons, and introduces a deterministic stabilizer to induce a fake stationary regime.
result SVIEs do not exhibit a strong stationary regime unless the kernel is constant or degenerate, but a fake stationary regime can be achieved with a deterministic stabilizer.
In this paper, we present our approach to solve a physics-based reinforcement learning challenge "Learning to Run" with objective to train physiologically-based human model to navigate a complex obstacle course as quickly as possible. The environment is computationally expensive, has a high-dimensional continuous actio…
Optimism stabilizes Thompson Sampling for adaptive inference in multi-armed bandits.
problem Subtle inferential properties of Thompson Sampling under adaptive data collection.
method Introduced optimism as a key mechanism to restore stability and validity of inference.
result Suitably implemented optimism stabilizes Thompson Sampling and enables asymptotically valid Wald inference.
We introduce a new recursive aggregation procedure called Bernstein Online Aggregation (BOA). The exponential weights include an accuracy term and a second order term that is a proxy of the quadratic variation as in Hazan and Kale (2010). This second term stabilizes the procedure that is optimal in different senses. We…
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion problem, i.e., the underlying true matrix is identifiable. We answer the question fro…
We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a non-deterministic and time inhomogeneous compensator. The BSDE generator function c…
Bayesian MoE framework improves LLMs' uncertainty detection.
problem Brittleness and overconfidence in deterministic routing of LLMs.
method Structured Bayesian routing in weight-space, logit-space, and selection-space.
result Significant improvements in routing stability, calibration, and OoD detection.
Recurrent neural networks trained on regular languages exhibit stable states that can recover from noise.
problem Stability of internal states in recurrent neural networks trained on regular languages.
method Empirical study with analysis of network activation and transitions between states.
result Recurrent neural networks trained on regular languages can recover from random perturbations and maintain stable states.
Online algorithms stabilize in feedback loops of performative prediction.
problem Feedback loops in algorithmic predictions influence data distributions.
method Martingale argument and randomization to avoid distributional assumptions.
result No-regret algorithms converge to performatively stable equilibria.
Chatter identification and detection in machining processes has been an active area of research in the past two decades. Part of the challenge in studying chatter is that machining equations that describe its occurrence are often nonlinear delay differential equations. The majority of the available tools for chatter id…
Paper uses SAC and DDPG to optimize cryptocurrency portfolios.
problem Adapting to volatile and nonlinear cryptocurrency markets.
method Reinforcement learning with SAC and DDPG algorithms.
result SAC and DDPG outperform traditional strategies in cryptocurrency markets.
Randomness is crucial for stability in learning and statistics, especially for differential privacy.
problem Quantifying the amount of randomness needed for algorithmic stability.
method Weak-to-strong boosting theorem for stability, characterizing randomness complexity of PAC Learning.
result Randomness complexity is tightly controlled by the best replication probability of any deterministic algorithm solving the task.
Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrica…
Adaptive optimal control of nonlinear dynamic systems with deterministic and known dynamics under a known undiscounted infinite-horizon cost function is investigated. Policy iteration scheme initiated using a stabilizing initial control is analyzed in solving the problem. The convergence of the iterations and the optim…
The need for parameter estimation with massive datasets has reinvigorated interest in stochastic optimization and iterative estimation procedures. Stochastic approximations are at the forefront of this recent development as they yield procedures that are simple, general, and fast. However, standard stochastic approxima…
This paper studies Thompson sampling's arm-pull dynamics and inference, revealing key differences from UCB algorithms.
problem Understanding the precise arm-pull dynamics in Thompson sampling algorithms.
method Developed new approaches to analyze the arm-pull count process and noise processes, including inverse process and reparametrization methods.
result Arm-pull count is asymptotically deterministic only for suboptimal or unique optimal arms, revealing a unifying principle of stability.
Extracts factors from Treasury yields using ML techniques.
problem Understanding factors underlying Treasury yields.
method Nonnegative Matrix Factorization (NMF) and clustering.
result Factors identified through NMF and clustering.
In the present paper and the companion paper [8] a probabilistic (statistical mechanical) approach to the study of canonical metrics and measures on a complex algebraic variety X is introduced. On any such variety with positive Kodaira dimension a canonical (birationally invariant) random point processes is defined and…