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 …
We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved explicitly by strategies of threshold type.
Improves early stopping in deep networks by adjusting stepsizes.
problem Epoch-wise double descent in deep networks.
method Analytical and empirical study of bias-variance tradeoffs in different network layers.
result Eliminating epoch-wise double descent through adjusting stepsizes of different layers improves early stopping performance.
Optimizes timing for buying and selling assets with a trailing stop.
problem Timing optimal buy and sell points for assets with a trailing stop.
method General linear diffusion framework, optimal double stopping problem, numerical method.
result Proves the optimality of using a sell limit order in conjunction with the trailing stop.
Hybrid regularization avoids double descent in random feature models.
problem Avoiding the double descent phenomenon in random feature models.
method Combines early stopping and weight decay, using GCV for hyperparameter selection.
result Hybrid method successfully avoids double descent and achieves comparable generalization.
New invariant stops certain types of geometric transformations.
problem Obstructing decomposable Lagrangian cobordisms.
method Defined an invariant for Legendrian links.
result Obstructs decomposable Lagrangian cobordisms.
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…
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.
This paper analyzes optimal stopping regions for American options with Poisson exercise opportunities.
problem Analyzing the optimal stopping regions for American options with Poisson exercise opportunities.
method Computing identities related to the first Poisson arrival time to an interval and applying them to the computation of the optimal strategies.
result Explicit expressions of the stopping and continuation regions and the value function are obtained.
This paper studies the timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We solve an optimal double stopping problem to determine the optimal times to enter and subsequently exit the market, when prices are driven by an exponential Ornstein-Uhlenbeck process. In addition, we analy…
Paper offers anytime-valid inference for causal parameters using DML.
problem Classic DML is only valid asymptotically for a fixed sample size.
method Time-uniform DML results for anytime-valid inference.
result Valid inference at any arbitrary stopping time.
Random Forests automatically prune a latent 'true' tree, explaining their overfitting without tuning.
problem Difficulty in building bad Random Forests and overfitting without apparent consequences.
method Bootstrap aggregation and model perturbation in Random Forests.
result Randomized ensembles implicitly perform optimal early stopping out-of-sample, explaining overfitting.
Double descent risk in L2-regularized models explained and mitigated.
problem Risk of overparameterized models in machine learning.
method Analysis of L2-regularized models, two-layer neural networks, and CNNs.
result Double descent risk in L2-regularized models can be explained and mitigated by adjusting regularization strengths.
Study optimal trading strategies for mean-reverting spreads using integral equations.
problem Optimal timing for trading mean-reverting price spreads.
method Utilized local time-space calculus and nonlinear integral equations of Volterra-type.
result Derived optimal boundaries for trading strategies.
This paper explains why double descent sometimes occurs weakly or not at all from an optimization perspective.
problem Understanding the role of optimization in the phenomenon of double descent.
method Investigates model-wise double descent from an optimization perspective, proposing a unified explanation for its occurrence.
result Model-wise double descent is observed if and only if the optimizer can find a sufficiently low-loss minimum.
This paper explains double descent in linear neural networks, identifying new factors.
problem Understanding double descent in linear neural networks.
method Gradient flow derivation and necessary conditions for double descent.
result Singular values of input-output covariance matrix are important for double descent in two-layer models.
Lewis and Mordecki have computed the Wiener-Hopf factorization of a Lévy process whose restriction on ]0,+∞[ of their Lévy measure has a rational Laplace transform. That allows to compute the distribution of (Xt,inf0≤s≤tXs). For the same class of Lévy processes, we compute the distribution of $ (…
Adversarial training overfits, harming robustness; early stopping fixes this.
problem Adversarial robustness in deep learning overfits to training data.
method Empirical study of adversarially trained deep networks.
result Overfitting to training data harms robust performance in adversarial training.
The paper explains why futures prices often differ from spot prices in grain markets.
problem Non-convergence of futures and spot prices in grains markets.
method Incorporates stochastic spot price and storage cost, solves an optimal double stopping problem.
result Explicit no-arbitrage prices for shipping certificates and futures contracts are derived.
Study negative discount rate effects on perpetual options in Lévy models.
problem Negative discount rate impacts perpetual American and Swing options in Lévy models.
method Analyze perpetual American and put options in exponential Lévy models with negative discount rate, identify critical continuation prices, and generalize to Swing type problems.
result Double continuation region arises in negative discount rate cases, identified by critical prices.
This paper studies the optimal VIX futures trading problems under a regime-switching model. We consider the VIX as mean reversion dynamics with dependence on the regime that switches among a finite number of states. For the trading strategies, we analyze the timings and sequences of the investor's market participation,…
The paper optimizes dynamic scheduling for ring architectures in deep learning training.
problem Optimizing deep learning training times with ring architectures.
method Formulated a non-convex, non-linear, NP-hard integer programming problem and developed a doubling heuristic.
result Dynamic scheduling can significantly reduce job completion times in ring architectures.
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.
Study optimal trading times for mean-reverting prices with deadlines.
problem Optimal timing strategies for mean-reverting price processes with deadlines.
method Solve optimal double stopping problems with sequential deadlines using local time-space calculus.
result Derive optimal trading boundaries for long-short, short-long, and chooser strategies.
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.
Neural networks optimize stopping boundaries in financial instruments.
problem Optimizing stopping boundaries in financial instruments.
method Deep neural networks and empirical risk minimization for parameterizing stopping boundaries.
result Proved existence of stopping boundary under natural assumptions.
The paper provides bounds for pricing Guaranteed Annuity Options under stochastic interest and mortality rates.
problem Valuation of Guaranteed Annuity Options in a correlated stochastic environment.
method Employing doubly stochastic stopping times and a change of measure, the authors derive general price bounds for GAOs.
result Derivation of general price bounds for GAOs using a conditioning approach for the lower bound and arithmetic-geometric mean inequality for the upper bound.
Sustaining efficiency and stability by properly controlling the equity to asset ratio is one of the most important and difficult challenges in bank management. Due to unexpected and abrupt decline of asset values, a bank must closely monitor its net worth as well as market conditions, and one of its important concerns …
New method stops experiments early for harm in diverse groups.
problem Early stopping of experiments for harmful treatment effects in diverse populations.
method Causal machine learning approach (CLASH) for early stopping.
result CLASH effectively stops experiments early for harmful treatment effects in diverse groups.
A survey of existing methods for stopping active learning (AL) reveals the needs for methods that are: more widely applicable; more aggressive in saving annotations; and more stable across changing datasets. A new method for stopping AL based on stabilizing predictions is presented that addresses these needs. Furthermo…
Analyzes the generalization and training errors of the random feature model over time.
problem Understanding the temporal behavior of generalization and training errors in deep learning.
method Uses Cauchy complex integral representations and random matrix methods based on linear pencils.
result Analytical solution of the full time-evolution path of generalization and training errors.
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 …
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.
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.
New algorithm solves complex stopping problems with robust optimization.
problem Solving complex stochastic optimal stopping problems.
method Simulation-based robust optimization with exact reformulation as a zero-one bilinear program.
result Developed polynomial-time heuristics and algorithms for practical solution.
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.
The strategy of early stopping is a regularization technique based on choosing a stopping time for an iterative algorithm. Focusing on non-parametric regression in a reproducing kernel Hilbert space, we analyze the early stopping strategy for a form of gradient-descent applied to the least-squares loss function. We pro…
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.
Solves optimal stopping problem for financial technical analysis.
problem Optimal stopping problem for technical analysis models.
method Wide-class dynamics modeling support/resistance lines.
result Solution to optimal stopping problem for technical analysis.
The paper solves recursive optimal stopping problems in stock trading.
problem Optimal stopping in recursive optimal stopping problems with applications to stock trading.
method Introduced a class of recursive optimal stopping problems and showed well-posedness in a Markovian setting. Determined optimal stopping rules in stock trading models.
result The value function is the unique solution to a fixed point problem and an optimal stopping time exists.
Diffusion models don't overfit, contrary to expectations.
problem Understanding generalization in diffusion models.
method Fundamental impossibility results and analysis of score matching.
result Diffusion models exhibit classical U-shaped loss curve, not double descent.
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
Study proposes a stopping criterion for active learning based on error stability.
problem Improving predictive performance in active learning by adaptively annotating samples.
method Proposes a stopping criterion based on error stability for Bayesian active learning.
result Demonstrates the proposed criterion stops active learning at the appropriate timing for various models and datasets.
Dynamic programming for optimal stopping under distribution constraints.
problem Optimal stopping with distributional constraints.
method Reformulating as measure-valued martingales and stochastic control problem.
result Established dynamic programming principle.
Adaptive rule improves kernel-based gradient descent performance.
problem Improving convergence speed of kernel-based gradient descent algorithms.
method Empirical effective dimension for stopping rule, learning theory analysis, integral operator approach.
result Optimal learning rates and iteration bounds for KGD with adaptive stopping rule.
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…
Dual martingales improve primal optimal stopping problem efficiency.
problem Optimal stopping problem in the primal formulation.
method Investigation of dual martingales to improve primal methods.
result Accurate dual martingale approximations reduce primal problem variance.
Early stopping improves logistic regression's calibration and consistency in high dimensions.
problem Improving the statistical performance of gradient descent in overparameterized logistic regression.
method Investigates the effects of early stopping on gradient descent in logistic regression.
result Early-stopped gradient descent is well-calibrated and statistically consistent, while asymptotic gradient descent is not.