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 problem”
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.
Solves consumption-investment problem with random horizon under Epstein-Zin preferences.
problem Maximizing consumption and investment under random time horizons with Epstein-Zin utility.
method Backward stochastic differential equations with superlinear growth on unbounded random horizons.
result Optimal strategies differ significantly when moving from fixed to random time horizons.
Proves uniqueness of certain spacetime solutions with extremal horizons.
problem Proving uniqueness of extremal Schwarzschild de Sitter spacetime solutions.
method Analytic proof in four and higher dimensions, spectral problem for hyperbolic surfaces.
result Proves extremal Schwarzschild de Sitter solutions are unique up to identifications.
Regularized greedy policies outperform classical greedy in finite-horizon bandit problems.
problem Optimizing decision-making in sequential experiments with finite time constraints.
method Developed regularized greedy algorithms for multi-armed Bernoulli bandits.
result Calibrated regularized greedy policies consistently match or outperform state-of-the-art algorithms.
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…
Optimal dividend strategy found for a fund with a finite time horizon.
problem Optimal dividend strategy for a fund with a finite time horizon.
method Characterized value function as unique solution to Hamilton-Jacobi-Bellman equation; Skorokhod reflection at time-dependent boundary.
result Optimal dividend strategy realized by Skorokhod reflection of fund's value at a time-dependent boundary.
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…
Proves conditions for Cauchy horizons in low-regularity spacetimes.
problem Conditions for the existence of Cauchy horizons in spacetimes with low regularity.
method Analyzes the relationship between complete Cauchy hypersurfaces, almost closed causal curves, and points at infinity.
result Wald's conjecture reformulated as a PDE problem about Cauchy horizons.
New method avoids high variance in infinite-horizon off-policy estimation.
problem High variance in importance sampling for long-horizon problems.
method Applies IS directly on stationary state-visitation distributions.
result Developed a novel approach to estimate density ratio.
Short-horizon bias causes meta-optimization to favor small learning rates.
problem Short-horizon bias in meta-optimization leads to suboptimal learning rates.
method Analyzes a noisy quadratic cost function and runs meta-optimization experiments on benchmark datasets.
result Meta-optimization chooses too small a learning rate, even with a long time horizon.
New insights into black hole horizons from asymptotic expansions.
problem Understanding the geometry of black hole horizons.
method Proving the asymptotic expansion of spacetime metrics at non-degenerate Killing horizons.
result The full asymptotic expansion of smooth vacuum metrics at non-degenerate Killing horizons is determined by the horizon geometry.
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.
We study the problem of stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. Specifically, we consider solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial data prescribed on a Cauchy hypersurface …
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.
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.
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.
We present a new infinite class of near-horizon geometries of degenerate horizons, satisfying Einstein's equations for all odd dimensions greater than five. The symmetry and topology of these solutions is compatible with those of black holes. The simplest examples give horizons of spatial topology S^3xS^2 or the non-tr…
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.
Study optimal switching under ambiguity in finance.
problem Optimal switching problems under ambiguity in finance.
method Use multidimensional reflected backward stochastic differential equations (RBSDEs) to characterize the optimal switching.
result Value function of optimal switching under ambiguity coincides with solutions to multidimensional RBSDEs with negative switching costs.
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.
We consider solutions to the linear wave equation on a suitable globally hyperbolic subset of an extreme Reissner-Nordstrom spacetime, arising from regular initial data prescribed on a Cauchy hypersurface crossing the future event horizon. We obtain boundedness, decay, non-decay and blow-up results. Our estimates hold …
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.
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…
This paper improves LSTM networks for long-term forecasts.
problem Challenges in long-horizon forecasting using LSTM networks.
method Expectation-biased LSTM architectures and methods.
result Significantly improved long-horizon forecasting performance.
Minimal surfaces connect to horizons and electrostatic systems.
problem Connecting minimal surfaces to horizons and electrostatic systems.
method One-parameter min-max problem for area functional, inequality relating area and charge.
result Minimal surfaces of index one are related to unstable horizons in electrostatic systems.
Study optimal liquidation in uncertain timeframes, minimizing risk and costs.
problem Minimizing risk and costs in liquidating assets with uncertain termination.
method Analyzes three scenarios using Almgren-Chriss model, verifies viscosity solutions for HJB equation.
result Characterizes value function as unique viscosity solution of HJB equation.
Heterotic horizons preserving 4 supersymmetries have sections which are T^2 fibrations over 6-dimensional conformally balanced Hermitian manifolds. We give new examples of horizons with sections S^3 X S^3 X T^2 and SU(3). We then examine the heterotic horizons which are T^4 fibrations over a Kahler 4-dimensional manifo…
Paper proves existence of anisotropic dynamical horizons in gravitational collapse.
problem Existence of apparent horizons in gravitational collapse.
method Scale-critical hyperbolic method and non-perturbative elliptic techniques.
result Smooth and spacelike apparent horizons emerge from general initial data in gravitational collapse.
New approach confirms Kruskal-Szekeres extension for Schwarzschild spacetime.
problem Confirming the Kruskal-Szekeres extension for Schwarzschild spacetime.
method Reformulating the problem as an ODE and showing the ODE admits a solution if and only if the horizon is non-degenerate.
result Photon surfaces approaching the Killing horizon must necessarily cross it.
The study classifies compact Cauchy horizons in vacuum spacetimes.
problem Classifying compact Cauchy horizons in vacuum spacetimes.
method Complete classification theorem based on topology and null generators.
result Different cases of compact Cauchy horizons with specific manifolds and spacetime properties.
Solves expert prediction problem for 4 experts in finite time horizon.
problem Expert prediction problem in finite horizon with 4 experts.
method Solves nonlinear PDE, shows solution, proves Nash equilibrium and regret conjectures.
result Proves Finite vs Geometric regret conjecture for and shows comb strategies are optimal.
Two new algorithms improve model-free RL for infinite-horizon MDPs.
problem Learning in infinite-horizon average-reward MDPs.
method Two model-free algorithms for infinite-horizon average-reward MDPs.
result Improved regret bounds for model-free RL in MDPs.
Horizon is Facebook's open RL platform for large, slow feedback datasets.
problem Training RL models with large, slow feedback datasets.
method End-to-end RL platform with workflows, data preprocessing, distributed training, etc.
result RL models trained with Horizon significantly outperform supervised learning systems.
The Infinite Horizon Investment-Consumption Problem for Epstein-Zin Stochastic Differential Utilityq-fin.MF
Investment and consumption strategy for risk-averse agents with Epstein-Zin utility.
problem Optimal investment and consumption strategy for Epstein-Zin utility.
method Detailed introduction to Epstein-Zin utility, existence and uniqueness proof, verification argument.
result Existence and uniqueness of optimal solution for Epstein-Zin utility under certain parameter restrictions.
UCRL-WVTR tackles long-term reinforcement learning with general approximations, achieving horizon-free and instance-dependent regret bounds.
problem Long-term reinforcement learning with general function approximations.
method UCRL-WVTR proposes a novel algorithm, UCRL-WVTR, with weighted value-targeted regression and a high-order moment estimator.
result Achieves horizon-free and instance-dependent regret bounds matching minimax lower bounds up to logarithmic factors.
Study of marginally trapped surfaces in a perturbed Schwarzschild spacetime.
problem Understanding marginally trapped surfaces in perturbed Schwarzschild spacetime.
method Developed a method to study spacelike surfaces in a double null coordinate system.
result For every incoming null hypersurface nearly spherically symmetric, there exists a unique embedded marginally trapped surface.
Study wave equations on compact Cauchy horizons with unique solutions.
problem Existence and uniqueness of solutions to wave equations near compact Cauchy horizons.
method Energy estimates and Cauchy horizon analysis for wave equations on vector bundles.
result Unique solution to wave equations on globally hyperbolic region if initial data is given on Cauchy horizon.
This review tackles long horizon forecasting in time series analysis using deep learning.
problem Long horizon forecasting in time series analysis.
method Incorporates deep learning techniques such as trend, seasonality, Fourier and wavelet transforms, and various model architectures.
result LHF is an error propagation problem, with models like xLSTM and Triformer showing better performance.
We find a simple strategy approximating optimal portfolio for short time horizons.
problem Optimizing portfolios in incomplete markets with general utility functions.
method Closed-form formula derived from HJB PDE, approximated by sub- and super-solutions.
result Approximation formula for optimal trading strategy is accurate for small time horizons.
Extends utility maximization theory for infinite horizons without strong no-arbitrage assumptions.
problem Maximizing lifetime utility from wealth over an infinite horizon.
method Develops a duality theory using deflators and supermartingale properties, extending previous work.
result Establishes a strong duality theorem for infinite horizon utility maximization under minimal no-arbitrage assumptions.
Optimal dividend strategy with capital injections over a finite time horizon.
problem Maximizing profits from dividends and minimizing costs of capital injections.
method Relating the problem to an optimal stopping problem for a drifted Brownian motion absorbed at the origin.
result The optimal dividend strategy is triggered by a moving boundary derived from the stopping problem.
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 …
Clarifies PSRL for infinite horizon problems without fixed episodes.
problem Applying PSRL in environments without fixed episodes.
method Review and critique of existing results and algorithms.
result Suggests PSRL can achieve bounds under certain assumptions.
We prove that compact Cauchy horizons in a smooth spacetime satisfying the null energy condition are smooth. As an application, we consider the problem of determining when a cobordism admits Lorentzian metrics with certain properties. In particular, we prove a result originally due to Tipler without the smoothness hypo…
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.
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.
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.