Paper optimizes industrial refrigeration using adaptive exploration.
problem Challenges in optimizing real-time industrial processes with unknown characteristics and safety constraints.
method Adaptive and explorative real-time optimization framework with Gaussian process uncertainty quantification.
result Approach increases energy efficiency of refrigeration process, approximating complete information solutions.
The paper studies time-optimal problems on specific Lie groups, describing orbits and integrals.
problem Time-optimal control problems on two-step Carnot groups.
method Description of co-adjoint orbits, Casimir functions, and integrals for the Hamiltonian system.
result Characterization of the flow and constancy of solutions for two-dimensional co-adjoint orbits.
New continuous-time optimization algorithms converge in finite time to local minima.
problem Finding local minima in optimization problems.
method Discontinuous dynamical systems with finite-time convergence via Lyapunov-based differential inequality.
result Finite-time convergence to strict local minima with provable settling time.
New method solves KP problem using global Cartan decompositions.
problem Solving time-optimal unitaries for targets in semi-simple Lie groups.
method Global Cartan decompositions of symmetric spaces for optimal control.
result Analytical solutions for time-optimal unitaries under specific conditions.
In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions. Motivated by problems in geometric group theory, we characterize extremal curves, d…
Enhances quantum circuit synthesis using deep learning and geometric methods.
problem Optimizing quantum circuits for time efficiency.
method Combining deep learning with geometric control techniques.
result Improved time-optimal control in quantum circuit synthesis.
We consider in this paper the regularity problem for time-optimal trajectories of a single-input control-affine system on a n-dimensional manifold. We prove that, under generic conditions on the drift and the controlled vector field, any control u associated with an optimal trajectory is smooth out of a countable set o…
We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By lifting the problem from the state space to the space of unitary gates realising the…
ARTEO algorithm optimizes safety-critical systems with uncertainty.
problem Decision-making under uncertainty with safety constraints in real-time optimization.
method ARTEO algorithm uses multi-armed bandits as a mathematical programming problem subject to safety constraints, learning unknown characteristics through exploration and incorporating uncertainty quantification.
result ARTEO achieves less cumulative regret with accurate and safe decisions.
AuON is a linear-time optimizer that improves upon Muon's performance without approximate orthogonal matrices.
problem High memory and computational costs of orthogonal momentum updates.
method AuON uses normalized nonlinear scaling and a 'emergency brake' to handle exploding attention logits.
result AuON achieves strong performance without approximate orthogonal matrices, preserving structural alignment and reconditioning.
We consider remodeling the planar search patterns, in the presence of the river-type perturbation represented by the weak vector field, basing on the time-optimal paths as Finslerian solutions to the Zermelo navigation problem via Randers metric.
A new algorithm approximates optimal stopping problems with semi-tractable complexity.
problem Approximating the value of optimal stopping problems in discrete and continuous time.
method Weighted Stochastic Mesh (WSM) Algorithm for discrete and continuous time optimal stopping problems.
result WSM leads to semi-tractable complexity in discrete cases, with complexity bounded by ε−4logd+2(1/ε). Optimal control theory improves machine teaching efficiency.
problem Finding the shortest training sequence for a sequential learning algorithm to reach a target model.
method Formulated as a time-optimal control problem, leveraging optimal control theory and computational tools.
result Optimal training sequences can vastly outperform existing heuristics.
In this paper, we examine higher order difference problems. Using the "squeezing" argument, we derive both Euler's condition and the transversality condition. In order to derive the two conditions, two needed assumptions are identified. A counterexample, in which the transversality condition is not satisfied without th…
This study examines abnormal geodesics in 2D-Zermelo navigation problems, revealing their role in separating time minimal and maximal curves.
problem The role of abnormal geodesics in planar Zermelo navigation problems with strong current.
method Geometric time optimal control approach, focusing on the heading angle of the ship.
result Abnormal geodesics separate time minimal and maximal curves, and are both small-time minimizing and maximizing.
Researchers describe Casimir functions for 3- and 4-step nilpotent Lie groups.
problem Understanding Casimir functions for free nilpotent Lie groups of steps 3 and 4.
method Construction of Casimir functions for free nilpotent Lie groups of steps 3 and 4.
result For 3-step groups, coadjoint orbits are fully described as affine subspaces or direct products of quadrics.
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
Researchers find optimal paths on a specific geometric group.
problem Finding optimal paths on a Cartan group with a sub-Finsler quasimetric.
method Using the Pontryagin Maximum Principle in coordinates of the first kind.
result They found extremals for arbitrary left-invariant sub-Finsler quasimetrics.
Paper proposes new γ-regret measure for non-episodic RL.
problem Measuring performance in non-episodic RL environments.
method Introduces γ-regret as a new performance measure and derives bounds. result Closed the gap between lower and upper bounds for γ-regret. A new RL method handles uncertainty and constraints in real-time optimization.
problem Real-time optimization under process uncertainty and constraints.
method Chance-constrained reinforcement learning to handle probabilistic state constraints.
result Satisfies process constraints with high probability in real-time.
We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the "stopper") who c…
Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strate…
We consider the Zermelo navigation problem on the ellipsoid of revolution (spheroid) in the presence of a perturbation W determined by a mild velocity vector field, ∣W∣<1, with application of Finsler metric of Randers type in the context of the corresponding optimal control represented by a time-efficient ship's he…
The paper studies problem of continuous time optimal portfolio selection for a incom- plete market diffusion model. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed using a limited number of fixed processes (mutual funds), for a m…
In this paper we study a sub-Finsler geometric problem on the free-nilpotent group of rank 2 and step 3. Such a group is also called Cartan group and has a natural structure of Carnot group, which we metrize considering the ℓ∞ norm on its first layer. We adopt the point of view of time-optimal control theory…
Solves time-optimal navigation on slippery slopes with cross gravitational wind.
problem Time-optimal navigation on a slippery cross slope under gravitational wind.
method New Finsler metric derived for the problem, considering both lateral and longitudinal gravitational effects.
result Conditions for strong convexity and purely geometric solution provided.
Researchers found optimal paths on a specific geometric group.
problem Finding optimal paths in a geometric group with a sub-Finsler metric.
method Used Pontryagin Maximum Principle for time-optimal control problem.
result Found extremals for left-invariant sub-Finsler metric.
Optimizes trading policies using future price forecasts.
problem Static reinforcement learning agents lack mechanisms for using price forecasts at inference time.
method FPILOT framework inspired by Model Predictive Control (MPC). Uses a predictive model to construct an allocation-based imagined return objective at each decision step.
result Consistent improvements in total return and risk-adjusted metrics across various policy learning algorithms.
Study uses RL to optimize investment with financial constraints, showing exploration benefits.
problem Optimal investment with financial constraints in continuous time.
method Reinforcement learning framework, focusing on Gaussian and truncated Gaussian distributions.
result Exploration leads to more dispersed wealth distribution with heavier tails, especially with smaller exploration parameters.
In certain circumstances tools of Riemannian geometry are sufficient to address questions arising in the more general Finslerian context. We show that one such instance presents itself in the characterisation of geodesics in Randers spaces of constant flag curvature. To achieve a simple, Riemannian derivation of this s…
Optimal estimator for discrete distributions from faulty batches.
problem Estimating discrete distributions from batches, some of which may be unreliable.
method First polynomial-time estimator achieving optimal accuracy in number of batches.
result Optimal estimation accuracy in polynomial time.
Optimal unimodal fitting for linear loss functions in a sequential, efficient manner.
problem Optimal unimodal transformation of univariate model scores under linear loss functions.
method Proposes a sequential approach to estimate the optimal rectangular fit for observed samples with each new sample.
result Sequential approach achieves optimal efficiency with logarithmic time complexity per iteration.
We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function induces decreasing impatience, we establish the existence of an equilibrium through …
The goal of this paper is to describe Zermelo's navigation problem on Riemannian manifolds as a time-optimal control problem and give an efficient method in order to evaluate its control curvature. We will show that up to change the Riemannian metric on the manifold the control curvature of Zermelo's problem has a simp…
Study optimal hedging for claims with random weights in discrete time.
problem Optimal hedging for claims with random weights in discrete time.
method Explicit recursive representation of optimal hedging strategy, without ND condition.
result Obtained explicit optimal hedging strategy in a recursive form.
In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy suitable variational inequalities which allow us to construct ε-optimal stopping tim…
Study describes periodic controls in step 2 sub-Finsler problems on Carnot groups.
problem Optimal control problems on step 2 Carnot groups with convex control sets.
method Describes Casimirs and symplectic foliations; shows extremal controls are periodic.
result Extremal controls are either constant or periodic.
Abstract: New methods for finding optimal controls in geometric problems on Lie groups.
problem Finding optimal controls for geodesics on Lie groups.
method Pontryagin maximum principle, (co)adjoint representation, geodesic vector field.
result Developed methods to find normal geodesics and locally optimal controls.
A great deal of academic and theoretical work has been dedicated to optimal liquidation of large orders these last twenty years. The optimal split of an order through time (`optimal trade scheduling') and space (`smart order routing') is of high interest \rred{to} practitioners because of the increasing complexity of t…
This work refines imitation learning to approximate optimal state-feedback policies for a quadcopter model.
problem Designing optimal control policies for complex systems like quadcopters.
method Supervised imitation learning using deep neural networks trained on optimal trajectories.
result Deep neural networks can approximate optimal state-feedback policies with high accuracy, even with two layers.
DeepPlace learns to place applications in clusters using RL.
problem Manual placement rules for scheduling are non-trivial and suboptimal.
method Uses Deep Reinforcement Learning to learn optimal placement rules.
result Reduces resource competition and optimizes cluster utilization.
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large deviation theory for the increments of empirical processes, we derive optimal convergenc…
New approach to optimal dividend timing with limited payouts.
problem Optimal timing of dividends with a constraint on the number of payouts.
method Developed a new type of time-inconsistent stochastic impulse control problem, derived the optimal solution in the precommitment sense, and formulated it as a sequential dynamic game.
result An equilibrium strategy derived for the problem, showing strong subgame perfect Nash equilibrium.
Optimizes search times by resetting agents when a threshold is reached.
problem Improving search efficiency in systems with thresholds.
method Develops a framework for correlated stochastic processes with threshold resetting.
result Optimal resetting can prevent larger losses and is applicable to various stochastic systems.
Paper develops a new method for optimal stopping in American options.
problem Optimal stopping in American options with singular generators.
method Entropy-regularized penalization scheme for reflected BSDEs with singular generators.
result Limit of the penalization scheme solves a reflected BSDE with a logarithmically singular generator.
In this research, we develop a trading strategy for the discrete-time optimal liquidation problem of large order trading with different market microstructures in an illiquid market. In this framework, the flow of orders can be viewed as a point process with stochastic intensity. We model the price impact as a linear fu…
Paper develops a new probabilistic method for American options using entropy regularization.
problem Finding optimal stopping times for American options with entropy regularization.
method Entropy-regularized penalization scheme based on Doob-Meyer-Mertens decomposition and reflected backward stochastic differential equations.
result Explicit convergence rates and policy improvement algorithm for American options.