We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to the finite horizon problems is optimal for the infinite horizon problems under th…
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48 results for “horizon optimization”
This paper studies the utility maximization problem with changing time horizons in the incomplete Brownian setting. We first show that the primal value function and the optimal terminal wealth are continuous with respect to the time horizon . Secondly, we exemplify that the expected utility stemming from applying th…
Careful tuning of the learning rate, or even schedules thereof, can be crucial to effective neural net training. There has been much recent interest in gradient-based meta-optimization, where one tunes hyperparameters, or even learns an optimizer, in order to minimize the expected loss when the training procedure is un…
In this paper, we propose to combine imitation and reinforcement learning via the idea of reward shaping using an oracle. We study the effectiveness of the near-optimal cost-to-go oracle on the planning horizon and demonstrate that the cost-to-go oracle shortens the learner's planning horizon as function of its accurac…
Optimizes investment under uncertain time horizons with non-concave utility.
problem Optimizing investment decisions with non-concave utility and uncertain time horizons.
method Established necessary and sufficient conditions for optimality, suggested recursive procedure for non-concave utility.
result Optimal investment strategies under uncertain time horizons exhibit multimodal distribution, indicating flexibility in switching between local maximizers.
The article calculates the near horizon limit of Wang--Yau quasi-local mass.
problem Calculating the near horizon limit of quasi-local mass.
method Utilizing the properties of the mean curvature vector and optimal embedding equation.
result Existence and uniqueness of optimal embedding and continuity of quasi-local mass.
Study optimal liquidation strategies with infinite horizon and regime switching.
problem Optimal liquidation with semimartingale strategies in a stochastic environment.
method Characterization of value function and optimal strategy via BSDEs with infinite horizon.
result Existence and uniqueness of optimal control problem solutions.
Reward tweaking optimizes behavior for long-term goals by adjusting the reward function.
problem Optimizing behavior for long-term goals in reinforcement learning with unstable long planning horizons.
method Reward tweaking learns a surrogate reward function that induces optimal behavior for the original task.
result Reward tweaking guides agents towards better long-term returns while planning for short horizons.
Growth-Optimal Strategies with Quadratic Friction Over Finite-Time Investment Horizonscond-mat.stat-mech
We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of capital invested in stocks within an interval around an ideal optimal investment. Th…
New optimizer SF-NorMuon matches tuned AdamW across various horizons.
problem Fixed learning-rate schedules in neural network training lead to strong path dependence and costly re-tuning.
method Schedule-Free Spectral Optimization (SF-NorMuon)
result SF-NorMuon outperforms tuned AdamW on 125M and 772M parameter models across different horizons.
This paper challenges the conventional wisdom of trend-following by showing that the medium-term horizon adds little value once short- and long-term components are included.
problem The conventional wisdom that more horizons improve diversification and performance is challenged.
method A Bayesian optimization framework reallocates exposure dynamically across horizons, optimizing horizon-level weights at the asset level and applying sparsity and turnover control for dynamic allocation across assets.
result The medium-term horizon contributes little incremental performance or diversification once short- and long-term components are included.
We aim to generalize the results of Cai and Nitta (2007) by allowing both the utility and production function to depend on time. We also consider an additional intertemporal optimality criterion. We clarify the conditions under which the limit of the solutions for the finite horizon problems is optimal among all attain…
This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do…
Study examines Wang-Yau quasi-local energy in strong fields near apparent horizons.
problem Examining the behavior of Wang-Yau quasi-local energy near apparent horizons in strong fields.
method Analyzing the limit of the Wang-Yau quasi-local energy as a spacelike surface approaches an apparent horizon, considering bounded coordinate functions and spacelike mean curvature.
result The limit of the Wang-Yau quasi-local energy falls into two cases: it blows up or remains finite, depending on whether the horizon can be isometrically embedded into .
WSqD extends learning rate schedules for large model training without fixed horizons.
problem Fixed learning rate schedules limit training horizon extension.
method WSqD replaces constant stable phase with a shifted inverse-square-root base, retaining linear cooldown.
result WSqD achieves minimax-optimal convergence rate and horizon-independence.
Study optimal portfolios in a non-Markovian regime-switching model with random time horizon.
problem Optimal portfolio selection in a market with non-Markovian regime-switching and random time horizon.
method Formulated as a constrained stochastic linear-quadratic optimal control problem, derived closed-form expressions for optimal portfolios and efficient frontier.
result Closed-form expressions for optimal portfolios and efficient frontier derived under non-Markovian regime-switching and random time horizon.
In this paper, we study optimal switching problems under ambiguity. To characterize the optimal switching under ambiguity in the finite horizon, we use multidimensional reflected backward stochastic differential equations (multidimensional RBSDEs) and show that a value function of the optimal switching under ambiguity …
New algorithm achieves asymptotically optimal regret without horizon dependence.
problem Horizon-free regret minimization for reinforcement learning.
method Proposes a new algorithm and proves a regret upper bound.
result Regret upper bound of \(\tilde O(\sqrt{SAK} + S^8A^3)\) with failure probability \(\delta\).
This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent …
Flexible forward improvement iteration for infinite time horizon Markovian optimal stopping problemsmath.PR
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.
Solves infinite horizon portfolio problem with path-dependent labor income.
problem Infinite horizon portfolio choice with path-dependent labor income.
method Solves an infinite dimensional stochastic optimal control problem using explicit solutions to the HJB equation.
result Explicit solutions to the optimal controls in feedback form are found.
A new Bayesian method optimizes time-dependent expensive functions with lookahead.
problem Maximizing a time-dependent, expensive oracle with limited evaluations.
method Recursive, two-step lookahead expected payoff (r2LEY) acquisition function.
result r2LEY outperforms myopic methods in synthetic and real-world datasets.
The problem of portfolio optimization is one of the most important issues in asset management. This paper proposes a new dynamic portfolio strategy based on the time-varying structures of MST networks in Chinese stock markets, where the market condition is further considered when using the optimal portfolios for invest…
Is Long Horizon Reinforcement Learning More Difficult Than Short Horizon Reinforcement Learning?cs.LG
Long horizon reinforcement learning is as hard as short horizon learning.
problem Understanding the difficulty of long horizon reinforcement learning problems.
method Introduced new concepts: ε-net for optimal policies and Online Trajectory Synthesis algorithm.
result Proved that sample complexity scales logarithmically with the planning horizon, refuting the conjecture.
Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizonmath.PR
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.
A new ML algorithm solves complex economic control problems.
problem Solving high-dimensional, finite-horizon stochastic control problems in economics.
method Deep neural network representation of optimal policy functions with three key features.
result Efficiently solves various economic control problems including recursive utility and growth models.
New algorithm learns optimal policies with just 1 episode, settling horizon-dependence in RL.
problem Understanding the sample complexity of reinforcement learning with horizon length.
method Developed an algorithm using only episodes to achieve PAC guarantee, leveraging connections between value functions in discounted and finite-horizon MDPs and novel perturbation analysis.
result Achieved the same PAC guarantee with only episodes of environment interactions, completely settling horizon-dependence in RL.
Implicit Finite-Horizon Approximation and Efficient Optimal Algorithms for Stochastic Shortest Pathcs.LG
New algorithms minimize regret in SSP with optimal sparse updates.
problem Minimizing regret in Stochastic Shortest Path models.
method Implicit finite-horizon approximation for analysis, model-free and model-based algorithms developed.
result Minimax optimal regret for both model-free and model-based algorithms.
We consider the problem of portfolio optimization in a simple incomplete market and under a general utility function. By working with the associated Hamilton-Jacobi-Bellman partial differential equation (HJB PDE), we obtain a closed-form formula for a trading strategy which approximates the optimal trading strategy whe…
New algorithm for RL with horizon-free reward-free exploration for linear MDPs.
problem Reward-free reinforcement learning with long planning horizons.
method Uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and moment estimator.
result Horizon-free sample complexity of for finding an -optimal policy.
FDS tackles long horizon hyperparameter optimization issues.
problem Memory scaling and gradient degradation in long horizon tasks.
method Forward-mode differentiation with sharing (FDS).
result Significantly outperforms greedy gradient-based alternatives.
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, to stu…
In this paper, we study optimal liquidation problems in a randomly-terminated horizon. We consider the liquidation of a large single-asset portfolio with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. Three different scenarios are analyze…
Paper solves Bayesian bandit problem with continuous-time limit and approximate policy.
problem Finding optimal policy in Bayesian bandit problems with large horizons.
method Reformulates Bayesian bandit problem as continuous Hamilton-Jacobi-Bellman (HJB) equation and proposes approximate Bayes-optimal policy.
result Approximate Bayes-optimal policy for large horizons with constant computational cost.
The paper analyzes risk measures and optimal reserve allocation strategies.
problem Risk measures and optimal reserve allocation across multiple lines of business.
method Formalizes expected maximum deficit, introduces implicitly bounded risk measures, and proposes capital allocation approaches.
result Theoretical results on static and dynamic coherence, convexity, and exact optimizations of aggregate minimum reserves.
UCRL2-VTR achieves nearly optimal regret for learning MDPs with linear function approximation.
problem Learning infinite-horizon average-reward MDPs with linear function approximation.
method UCRL2-VTR algorithm with Bernstein-type bonus.
result Achieves a regret of with matching lower bound.
Extends RL to random stopping times, improving optimization.
problem Real-world applications with random stopping times.
method Extended RL framework to random stopping times, derived new formulas.
result Improves optimization convergence with new formulas.
We examine optimal execution models that take into account both market microstructure impact and informational costs. Informational footprint is related to order flow and is represented by the trader's influence on the flow imbalance process, while microstructure influence is captured by instantaneous price impact. We …
The paper optimizes portfolios in a financial market with correlated assets using a stochastic volatility model.
problem Optimizing portfolios in a financial market with correlated assets and stochastic volatility.
method Derive a Hamilton-Jacobi-Bellman equation, use approximation methods, analyze value function using expansion of utility function, control error with second-order terms, generate close-to-optimal portfolio.
result Close-to-optimal portfolio generated using first-order approximation of utility function with controlled error.
This paper is concerned with offline reinforcement learning (RL), which learns using pre-collected data without further exploration. Effective offline RL would be able to accommodate distribution shift and limited data coverage. However, prior algorithms or analyses either suffer from suboptimal sample complexities or …
Study long-term asset liquidation behavior with external flows.
problem Investigate optimal liquidation in presence of external flows.
method Convergence analysis of BSDEs for value function and strategy.
result Long-term liquidation may not occur due to external flows.
New algorithm reduces offline RL data requirements significantly.
problem Optimizing policies using only historical data in reinforcement learning.
method Off-Policy Double Variance Reduction (OPDVR) algorithm.
result OPDVR achieves optimal sample complexity with episodes.
Derives time-averaged active inference from control principles.
problem Finite-horizon or discounted-surprise problems in active inference.
method Derives infinite-horizon, average-surprise active inference from optimal control principles.
result Unified objective functional for sensorimotor control.
A new model for heterogeneous populations optimizes consumption and investment over short horizons.
problem Optimizing consumption and investment in economies with a heterogeneous population over short time periods.
method Continuous-time general equilibrium framework with Brownian flow on a type space, solving vanishing-horizon problems under relative-income criteria.
result Existence and characterization of short-horizon Duesenberry equilibrium, with sharp asset-pricing implications.
In many finite horizon episodic reinforcement learning (RL) settings, it is desirable to optimize for the undiscounted return - in settings like Atari, for instance, the goal is to collect the most points while staying alive in the long run. Yet, it may be difficult (or even intractable) mathematically to learn with th…
This paper examines the volatility and covariance dynamics of cash and futures contracts that underlie the Optimal Hedge Ratio (OHR) across different hedging time horizons. We examine whether hedge ratios calculated over a short term hedging horizon can be scaled and successfully applied to longer term horizons. We als…
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and…
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.