This paper solves the best arm identification problem with both quick commitment and reward maximization.
problem Simultaneously identifying the best arm and minimizing regret in a stochastic Multi-Armed Bandit problem.
method Introduces Regret Optimal Best Arm Identification (ROBAI) and presents algorithms EOCP and its variants.
result Achieves asymptotic optimal regret and quick commitment to the optimal arm in both pre-determined and adaptive stopping times.
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.
Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times or randomized stopping times may not exist. This motivates us to cons…
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.
We study the problem of selling an asset near its ultimate maximum in the minimax setting. The regret-based notion of a perfect stopping time is introduced. A perfect stopping time is uniquely characterized by its optimality properties and has the following form: one should sell the asset if its price deviates from the…
Improved reinforcement learning with emergency stops.
problem Reducing exploration in reinforcement learning.
method Emergency stop mechanisms to reduce sample complexity.
result Significant improvement in sample complexity and speed.
Adaptive speculative decoding framework for LLMs using bandit algorithms.
problem Adaptive speculative decoding for LLMs to balance speed and quality.
method Formulated as a Multi-Armed Bandit problem, proposed UCBSpec and EXP3Spec algorithms.
result UCBSpec algorithm achieves optimal regret performance up to universal constants.
The paper tackles best arm identification with minimal regret in experiments.
problem Identifying the best arm with minimal regret in experiments.
method Information-theoretic techniques and Double KL-UCB algorithm.
result Achieves asymptotic optimality in identifying the best arm with minimal regret.
The paper explores trade-offs between regret and variance in online learning algorithms.
problem Investigating the trade-offs between regret and variance in online learning.
method Analysis of the Exponentially Weighted Average (EWA) algorithm and its variants.
result A variant of EWA either achieves negative regret or guarantees a logarithmic bound on both variance and regret.
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. We develop the first Bayesian Optimization algorithm, BLOSSOM, which selects between multiple alternative acquisition functions and traditional local optimization at each step. This is combined with a novel stopping condition based on expected regret. This pairing allows us to obtain the best characteristics of both lo…
Solves optimal stopping problem with Poisson constraints using jumps.
problem Optimal stopping with Poisson constraints and jumps.
method Penalized backward stochastic differential equation (PBSDE) with jumps, decomposition method based on Jacod-Pham, comparison theorem of BSDEs with jumps.
result Solves American option pricing in nonlinear markets with Poisson constraints.
A new algorithm balances exploration and exploitation in online decision-making.
problem Balancing exploration and exploitation in online decision-making.
method Proposed C4-UCB algorithm incorporating conservative mechanism. result Proved n-step upper regret bound for two situations.
Continuous-time optimal stopping solved with deep reinforcement learning
problem Optimal stopping problems in continuous time
method CARLOS (Continuous-time Adaptive Reinforcement Learning for Optimal Stopping)
result Higher prices than existing Bermudan solvers, approaching American upper bound
New algorithms improve stopping time for best arm identification.
problem Efficiently identifying the best alternative in experiments.
method Proposed algorithms with exponential-tailed stopping time.
result Proved that some algorithms never stop, leading to new methods.
We consider the optimal double stopping time problem defined for each stopping time S by $v(S)=\esssup\{E[ψ(τ_1, τ_2) | \F_S], τ_1, τ_2 \geq S \}$. Following the optimal one stopping time problem, we study the existence of optimal stopping times and give a method to compute them. The key point is the construction of …
Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.
problem Optimal stopping problems with finite-time horizon and state-dependent discounting.
method Linear diffusion process, time-homogeneous gain function, fine regularity properties, continuity and strict monotonicity proof.
result Proves continuity and strict monotonicity of the optimal stopping boundary under mild assumptions.
We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.
Solves optimal stopping for Gauss-Markov bridges using time-space transformation.
problem Optimal stopping problem of a Gauss-Markov bridge.
method Time-space transformation approach, Picard iteration algorithm.
result Lipschitz continuity of the optimal stopping boundary and its characterization.
We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of "put" type and the underlying dynamics follows a geometric Brownian motion. The op…
In this paper, we propose several "measurements" of the "non-stopping timeness" of ends g of previsible sets, such that g avoids stopping times, in an ambiant filtration. We then study several explicit examples, involving last passage times of some remarkable martingales.
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 tackles optimal stopping problems using reinforcement learning and singular control.
problem Continuous-time and state-space optimal stopping problems.
method Formulated as a singular control problem with randomized stopping times and penalized cumulative residual entropy.
result Identified unique optimal exploratory strategy through dynamic programming.
Early stopping method saves up to 75% computation time in policy search tasks.
problem Lengthy evaluation times in optimization problems, especially in robotics.
method A generalized early stopping criterion that only uses objective value at each time step.
result The method saves up to 75% computation time compared to no stopping.
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
Method calculates Parisian stopping times and option prices using Markov chains.
problem Computing distribution and pricing of Parisian stopping times under Markov processes.
method Continuous-time Markov chain approximation to solve for distribution and convergence analysis.
result Sharp convergence rate and efficient method for diffusion and jump models.
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.
The paper provides bounds on estimation error in a distributed online learning setting.
problem Estimating an unknown parameter in a distributed and online manner with finite sample guarantees.
method Proposes a distributed online estimation algorithm that improves accuracy through communication, providing non-asymptotic bounds on estimation error.
result Demonstrates a trade-off between estimation error and communication costs, and determines a stopping time for communication based on desired accuracy.
Algorithm identifies optimal stable matching in uncertain two-sided markets.
problem Sequential learning in two-sided markets with unknown preferences.
method Pure exploration approach with elimination-based algorithms exploiting partial preference information.
result Identification of pervasive stable matching for optimal stable matching identification.
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.
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…
This paper considers a time-inconsistent stopping problem in which the inconsistency arises from non-constant time preference rates. We show that the smooth pasting principle, the main approach that has been used to construct explicit solutions for conventional time-consistent optimal stopping problems, may fail under …
We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game wh…
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…
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
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.
Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. Modeling the price spread by an Orn…
In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length δ, the so called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise c…
A framework for robust exploration in reinforcement learning under ambiguity.
problem Optimal stopping under ambiguity in reinforcement learning.
method Continuous-time robust reinforcement learning framework using g-expectation and backward stochastic differential equations. result Constructs a robust exploratory stopping time approximating the optimal stopping time under ambiguity.
New algorithms use Gaussian processes to optimize stopping times in financial markets.
problem Optimizing stopping times in financial time series with specific applications.
method Gaussian and Deep Gaussian Process models to analytically evaluate optimal stopping value functions and policies.
result Proposed algorithms outperform benchmarks on various financial time series datasets.
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.
Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent may care only about states where she is still alive at the time …
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.
Given an initial (resp., terminal) probability measure μ (resp., ν) on Rd, we characterize those optimal stopping times τ that maximize or minimize the functional E∣B0−Bτ∣α, α>0, where (Bt)t is Brownian motion with initial law B0∼μ and with final distribution --once stop…
American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale representations are presented for short (seller's) and long (buyer's) positions in an Americ…
Improved algorithm for optimal stopping problems reduces runtime.
problem Optimal stopping problems with infinite time horizon and random discounting.
method Flexible forward improvement iteration with a variable look-ahead distance.
result The new algorithm converges and can significantly reduce runtime.
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.
The study reveals optimal early stopping behaviors in deep learning models.
problem Understanding optimal early stopping in deep learning models.
method Theoretical analysis of linear models and experimental validation.
result Two distinct behaviors of optimal early stopping time depending on model dimension relative to dataset features.