New approach to optimal stopping under bounded rationality, considering future events.
problem Optimal stopping with conditional objectives, e.g., survival or non-bankruptcy.
method Equilibrium approach for time-inconsistent optimization, generalizing Snell envelope.
result Equilibria are unique in finite time but non-uniqueness in infinite time.
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel representation for the solution of the optimal stopping problem. In particular, we …
The paper studies early stopping methods in linear contextual bandits.
problem Minimizing in-experiment regret and conducting robust post-experiment inferences in contextual bandits.
method The study proposes early stopping rules based on the Opportunity Cost and Threshold Method, using variances of estimators to quantify upper regret bounds.
result The proposed method provides a systematic approach to minimize in-experiment regret and conduct robust post-experiment inferences.
This work bounds the run-time of nonconvex optimization with early stopping.
problem Bounding the expected run-time of nonconvex optimization with early stopping.
method Derives conditions for well-defined early stopping based on validation function norms and bounds the expected number of iterations and gradient evaluations.
result Guarantees the validity of early stopping and provides bounds on the expected run-time for various optimization algorithms.
We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer. Moreover, conditions are provided under which the existence of an optimal stopping time…
We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a connection between the considered problem and a stopping problem of an associated…
Researchers find optimal stopping points for assets under non-exponential discounting.
problem Finding optimal stopping points for assets under non-exponential discounting.
method Constructing optimal equilibria for continuous-time stopping problems with specific conditions.
result Optimal equilibria are unique under certain conditions and can be characterized explicitly.
Proposes data-driven methods for estimating conditional expectations.
problem Estimating conditional expectations when underlying density is unknown.
method Data-driven techniques to directly estimate conditional expectations from training data.
result Extends data-driven method to solve nonlinear equations in stochastic optimization.
This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting-stopping and switching problems admit …
Study optimal stopping for diffusion processes using data-driven methods.
problem Optimal stopping for diffusion processes under unknown conditions.
method Data-driven approach, deriving upper and lower bounds on simple and cumulative regret.
result Verified minimax optimality and improved convergence rates.
Sharp risk bounds for early-stopping in Gaussian linear regression are derived.
problem Minimizing in-sample mean squared error in high-dimensional Gaussian linear regression.
method Early-stopped mirror descent (ESMD) with local Gaussian width bounds.
result Sharp risk bounds extend to early-stopped mirror descent for least squares estimator (LSE).
The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.
problem Characterizing and comparing different types of equilibria for time-inconsistent stopping problems.
method Analyzes log sub-additive discount functions and one-dimensional diffusion processes to derive necessary and sufficient conditions for weak equilibria and other types of equilibria.
result Conditions for weak equilibria and their implications for other types of equilibria are provided.
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an initial condition and view the problem as a stochastic control problem; we esta…
MUSE provides unbiased stopping estimates for optimal problems.
problem Estimating the utility of optimal stopping problems.
method Backward recursive construction of the Multilevel Unbiased Stopping Estimator (MUSE).
result MUSE achieves ε-accuracy with O(1/ε^2) computational cost.
BLOSSOM optimizes switching between local and Bayesian methods for faster convergence.
problem Optimizing function evaluations efficiently and converging to global minimum.
method Combines local and Bayesian optimization with a stopping condition based on expected regret.
result Achieves superior convergence and efficient use of function evaluations.
Early stopping improves neural networks' performance on binary classification tasks.
problem Improving shallow ReLU networks' performance on binary classification tasks.
method Gradient descent with early stopping on binary classification data.
result Gradient descent with early stopping achieves population risk arbitrarily close to optimal.
Study optimal stopping in random exploration, deriving HJB and designing a reinforcement learning algorithm.
problem Optimal stopping problem in continuous time with random exploration.
method Transformed optimal stopping to optimal control problem, derived HJB equation, designed reinforcement learning algorithm.
result Convergence rate of policy iteration and comparison to classical optimal stopping.
Study optimal stopping times under regime-switching models with constraints.
problem Optimal stopping times for discounted payoffs on a regime-switching geometric Brownian motion.
method Solve variational inequality to find value functions and optimal thresholds.
result Existence and expressions of optimal stopping times under specific conditions.
Study optimal stopping times for multi-dimensional processes with non-exponential discounting.
problem Optimal stopping in multi-dimensional processes with non-exponential discounting.
method Probabilistic potential theory to establish existence of optimal equilibria.
result Existence of optimal equilibria for multi-dimensional stopping problems.
DO-IQS recovers optimal stopping region from expert trajectories, addressing specific challenges.
problem Recovering optimal stopping region from expert trajectories with unknown gain functions.
method Dynamics-Aware Offline Inverse Q-Learning incorporating temporal information and confidence-based oversampling.
result Demonstrated performance on real and artificial data, including optimal intervention for critical events.
Paper solves a complex stopping problem using regularization and HJB equations.
problem Time-inconsistent mean-variance optimal stopping problem
method Vanishing regularization method to derive HJB equations and prove existence of solutions
result Formally recovers variational inequalities for original problem
Early stopping improves sample quality in latent diffusion models.
problem Latent diffusion models degrade sample quality with conventional early stopping.
method Analyzed the interaction between latent dimension and stopping time under Gaussian framework.
result Lower-dimensional representations benefit from earlier termination, higher-dimensional spaces require later stopping.
Optimal stopping strategy for a Lévy process near its supremum.
problem Predicting optimal stopping distance for a Lévy process.
method Characterization using scale functions and threshold analysis.
result Non-trivial stopping strategy based on a threshold.
New method models stopping times that can be equal with non-zero probability.
problem Standard stopping time models assume conditional independence, limiting flexibility.
method Modified Cox construction with bivariate exponential distribution.
result Created a family of stopping times that can be equal with positive probability.
The paper solves IRL for Bayesian stopping time problems.
problem Identifying optimal actions in Bayesian stopping time problems.
method Novel IRL framework using Bayesian revealed preferences.
result Identifies optimality and constructs cost function estimates.
A new method uses deep learning for optimal stopping problems.
problem Solving optimal stopping problems in financial mathematics.
method Deep primal-dual BSDE framework with a novel loss function.
result The method provides a true upper bound for the optimal value.
Study optimal stopping for group with diverse discount rates using an attitude function.
problem Optimal stopping for a group with diverse discount rates under an aggregation preference.
method Develop iterative approach using consistent planning for time-consistent equilibria.
result Characterize all time-consistent mild equilibria as fixed points of an operator.
Study optimal stopping for variable annuity contracts with discontinuous rewards.
problem Optimal timing to surrender a variable annuity contract with guaranteed minimum benefit.
method Analytical study of an optimal stopping problem with a discontinuous reward function, considering general fee and surrender charge functions.
result Characterization of the surrender region and its interrelation with fee and surrender charge functions.
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to a finite sequence of state-constrained optimal control problems with additional…
Probabilistic proof of smooth boundaries in optimal stopping problems.
problem Continuous differentiability of time-dependent optimal boundaries in optimal stopping problems.
method Local probabilistic arguments for a wider range of conditions.
result First probabilistic proof of continuous differentiability under general conditions.
Bayesian optimization stops when a solution is within ε of the optimum with high probability.
problem Stopping Bayesian optimization prematurely based on a probabilistic criterion.
method Introducing a (ε,δ)-criterion for stopping Bayesian optimization. result Bayesian optimization satisfies the (ε,δ)-criterion under mild assumptions. Direct method solves complex option pricing in changing market conditions.
problem Pricing financial options with changing market conditions.
method Reduces complex optimal stopping problems to simpler ones, finding explicit value functions.
result Simpler and more direct solution for option pricing in regime-switching models.
Optimality of threshold strategies proven for Lévy models with discounting.
problem Proving optimality of threshold strategies in Lévy models with discounting.
method Average problem approach to prove optimality of threshold strategies for Lévy models with continuous additive functional discounting.
result Simpler and neater proofs for qualitative properties of optimal thresholds in recursive optimal stopping problems.
CoRAS adapts image acquisition rates for accurate reconstruction.
problem Determining when enough measurements are collected for accurate image reconstruction.
method Adaptive acquisition rate selection based on reconstruction error probability.
result CoRAS achieves target stopping-time coverage with fewer measurements.
Study naive vs sophisticated agents stopping a diffusion process with time-inconsistent payoffs.
problem Time-inconsistent stopping problem for diffusion processes.
method Analyzes naive and sophisticated agents' strategies, proving equilibrium existence.
result Equilibrium strategies can be derived as fixed points of strategic reasoning operators.
New method finds optimal training stop point with noisy labeled data.
problem Finding optimal training stop point with noisy labeled data.
method Analyzed training accuracy rate changes for different noise ratios to identify a training stop region. Developed a heuristic algorithm based on a small-learning assumption.
result Identified optimal training stop point at or close to maximum obtainable test accuracy.
This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probabil…
Investment strategy optimization from discrete to continuous models.
problem Optimizing investment strategies and stopping times in both continuous and discrete settings.
method Characterized value functions via quadratic reflected BSDEs for continuous case, discretized BSDEs for discrete case, and derived uniform convergence rates.
result Uniform convergence and rate from discrete to continuous quadratic reflected BSDEs.
Suggests stopping criteria for feature selection using mutual information.
problem Automatic determination of optimal feature subset size and stopping criterion.
method Monitoring conditional mutual information (CMI) among groups of variables using Renyi's α-entropy.
result Easy to implement stopping criteria for feature selection.
The paper proves generalization bounds and stopping rules for self-selected data in reciprocal learning.
problem Generalization of learning algorithms using self-selected data.
method Proves universal generalization bounds using covering numbers and Wasserstein ambiguity sets.
result Provides stopping rules for reciprocal learning algorithms to ensure out-of-sample performance.
Analysis of cross-validation for early-stopped gradient descent in high-dimensional regression.
problem Inconsistency of GCV for early-stopped GD in high-dimensional least squares regression.
method Theoretical analysis of GCV and LOOCV applied to early-stopped GD in high-dimensional least squares regression.
result LOOCV converges uniformly to the prediction risk of early-stopped GD, while GCV is generically inconsistent.
Investors with anxiety about drawdowns may use stop-loss and trailing stops as optimal selling strategies.
problem Investors' anxiety about drawdowns affects optimal selling strategies.
method Mathematical analysis of optimal stopping with random discounting.
result Stop-loss and trailing stops can be optimal selling strategies under anxiety about drawdowns.
Develops new optimization techniques for decision-making under uncertainty.
problem Decision-making under uncertainty with complex cost functions and nested expectations.
method Introduces Multistage Conditional Compositional Optimization (MCCO) and develops multilevel Monte Carlo techniques.
result New optimization techniques reduce scenario complexity from exponential to polynomial growth.
IRKSN algorithm achieves sparse recovery with wider applicability conditions.
problem Sparse recovery challenges due to NP-hard nature and restrictive conditions.
method IRKSN algorithm based on k-support norm regularizer. result Achieves sparse recovery with explicit constants and standard linear rate.
This paper addresses the question of how an arbitrage-free semimartingale model is affected when stopped at a random horizon. We focus on No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) concept, which is also known in the literature as the first kind of non-arbitrage. For this non-arbitrage notion, we ob…
Modern proximal and stochastic gradient descent (SGD) methods are believed to efficiently minimize large composite objective functions, but such methods have two algorithmic challenges: (1) a lack of fast or justified stop conditions, and (2) sensitivity to the objective function's conditioning. In response to the firs…
We study the existence of optimal actions in a zero-sum game infτsupPEP[Xτ] between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem infτE(Xτ) for a class of sublinear expectations E(⋅) such as the G-expectation. We show that …
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as…