A new method solves complex control problems with random coefficients.
problem Solving LQ McKean-Vlasov control problems with random coefficients.
method Decomposes the problem into two decoupled stochastic optimal control problems.
result The sum of optimal controls of auxiliary problems equals the original problem's optimal control.
Paper studies optimal control for a specific geometric problem.
problem Optimal control problem associated with the Paneitz obstacle problem.
method Existence and regularity results for optimal controls.
result Existence of optimal controls and their properties.
Paper solves a control problem with robust methods.
problem Monotone mean-variance problems with stochastic coefficients.
method Finding saddle point through BSDEs with unbounded coefficients.
result Optimal control and value match mean-variance problems.
Motion planning and control are key problems in a collection of robotic applications including the design of autonomous agile vehicles and of minimalist manipulators. These problems can be accurately formalized within the language of affine connections and of geometric control theory. In this paper we overview recent r…
New control theory for self-path-dependent problems solves unique constraints.
problem Optimal control with self-path-dependent constraints in stochastic systems.
method Introduces new HJB equations for variational inequalities with historical maximum controls.
result Value functions are viscosity solutions to HJB equations under Lipschitz conditions.
Study of control problems on Carnot groups with SO(3) symmetry using geometric algebra.
problem Control problems on Carnot groups with SO(3) symmetry.
method Geometric algebra approach to understand geodesics and develop a control algorithm.
result New algorithm for local control developed.
Derives optimal control conditions using calculus of variations.
problem Optimizing Markov control in stochastic control problems.
method Calculus of variations approach to derive necessary conditions.
result Solves the Merton portfolio optimization problem.
Deep Galerkin Method estimates value function for mean-field control problem.
problem Optimal control of agents with average welfare as the objective.
method Apply DGM to estimate value function and distribution evolution.
result Neural network approximations converge to analytical solution.
We geometrically describe optimal control problems in terms of Morse families in the Hamiltonian framework. These geometric structures allow us to recover the classical first order necessary conditions for optimality and the starting point to run an integrability algorithm. Moreover the integrability algorithm is adapt…
New method solves nonseparable stochastic control problems.
problem Nonseparable and non-monotonic stochastic control problems.
method Scenario-decomposition solution framework using progressive hedging algorithm.
result Extends reach of stochastic optimal control.
We provide bounds on control learning error in stochastic systems.
problem Learning optimal controls in stochastic environments with uncontrolled parts.
method Dynamic programming and mean-field interpretation of neural networks.
result Non-asymptotic bounds on generalization error for stable overparametrised settings.
We explore a new method for discrete-time control problems using randomization and entropy.
problem Discrete-time linear-exponential quadratic Gaussian (LEQG) control problem.
method Introduce exploration through randomization and apply duality between free energy and relative entropy.
result Reduced LEQG problem to equivalent risk-neutral LQG control problem with entropy regularization.
New framework for policy gradient methods in continuous time reinforcement learning.
problem Addressing policy gradient methods for continuous time reinforcement learning.
method Control randomisation technique to derive policy gradient representation for various Markovian control problems.
result Demonstrated application to optimal switching problems in the energy sector.
Solves inventory control with unknown demand trend using singular control.
problem Optimally managing inventory with an unknown demand trend.
method Formulates as a stochastic control problem under partial observation, solves equivalent separated problem using transition between formulations, and applies viscosity theory.
result Constructs an optimal control rule and shows bounded Lipschitz continuity of free boundaries.
Abstract: Surveying connections between ML and Control Theory.
problem Addressing the intersection of Machine Learning and Control Theory.
method Develops connections through reinforcement learning, supervised learning, deep learning, and stochastic gradient descent.
result Machine Learning and Control Theory are interconnected, with ML solving large control problems and Control Theory providing tools for ML.
In stochastic control problems delicate issues arise when the controlled system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the controller knows when about the exogenous shocks and how and when she can act on this information. We propose to use Meyer-σ-fields as a flexi…
Optimal controls for conformal Laplacian obstacle problems on spheres and manifolds.
problem Optimal control of conformal metrics with constant scalar curvature.
method Analysis of optimal control problem on Riemannian manifolds with positive Yamabe invariant.
result Existence of smooth optimal controls inducing metrics with constant scalar curvature.
New method for handling multi-dimensional singular controls with jump costs in mean-field problems.
problem Handling jump costs in multi-dimensional singular controls.
method Introducing two-layer parametrisations to interpolate jumps on both distributional and pathwise levels.
result Derivation of a DPP and characterisation of the value function as a minimal super-solution to a quasi-variational inequality.
Langevin algorithms enhance training of deep neural networks for stochastic control problems.
problem Training acceleration for deep neural networks in stochastic control problems.
method Application of Langevin algorithms to minimize the loss of deep neural networks in stochastic control problems.
result Langevin algorithms improve training on various stochastic control problems.
The Noether theorem is extended to stochastic control problems using contact symmetries.
problem Stochastic optimal control problems.
method Exploiting jet bundles and contact geometry, the authors prove the existence of conserved quantities.
result Optimal control problems admit infinitely many conserved quantities in the form of local martingales.
New theory extends LQ control to non-exponential discount scenarios.
problem Time-inconsistent deterministic LQ control problems.
method Extended equivalent relationship to non-exponential discount functions, studied Riccati equation solvability.
result Existence and uniqueness of linear equilibrium for time-inconsistent LQ problem.
The paper defines and solves time-inconsistent stopping control problems in multi-dimensional diffusion models.
problem Time-inconsistent problems in control and stopping strategies.
method Formal definition of weak equilibria, extended HJB system, and verification methodology.
result Explicit equilibrium solutions and existence of non-constant equilibria.
Method solves learning problem with hierarchical control objectives.
problem Learning high-dimensional nonlinear functions with model validation accuracy.
method Successive approximation method in functional spaces for hierarchical optimal control.
result Nested algorithm for solving optimal control problem.
Study on SU(2) group's Lorentzian problem, focusing on controllability and extremals.
problem Left-invariant Lorentzian problem on SU(2) group.
method Addressing complete controllability, existence of length maximizers, extremals.
result Results on controllability and extremals for the Lorentzian problem.
Study of multidimensional control problems with reflection controls.
problem Solving control problems with reflection controls in multidimensional settings.
method Gradient descent algorithm for polytope approximations, data-driven domain estimator, episodic learning algorithm.
result Data-driven solutions for unknown diffusion dynamics with sublinear regret.
Investigates optimal strategies for behavioral control problems with finite variation controls.
problem Behavioral singular stochastic control problems with finite variation controls.
method Abstract framework, applied to storage management and portfolio investment problems, using CPT preferences and Skorokhod representation theorem.
result Existence of optimal strategies for various goal functionals, including CPT preferences.
Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo sampling. We approximate the time-dependent controls as feedforward neural networ…
Formula found for heat equation control and backward problems.
problem Exact control of nonhomogeneous backward heat equations.
method Time analyticity and eigenfunctions of the Laplacian.
result Explicit formula for control function in terms of heat kernel.
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop the explicit solution for this class of problem. The revealed optimal control poli…
New deep learning method solves stochastic control problems.
problem Solving strongly coupled FBSDEs for stochastic control.
method Modified deep BSDE method with new loss function.
result Empirical convergence of the new method for three problems.
Study optimizes trading in multiple assets with cross-effects.
problem Optimizing trade execution in multiple assets with cross-impact effects.
method Formulated as a stochastic control problem, extended to progressively measurable controls, solved using linear-quadratic control theory.
result Cross-hedging effects can be optimal, e.g., trading in an asset without an initial position.
Nonlinear optimal control problems are often solved with numerical methods that require knowledge of system's dynamics which may be difficult to infer, and that carry a large computational cost associated with iterative calculations. We present a novel neurobiologically inspired hierarchical learning framework, Reinfor…
We present a novel technique to solve the problem of managing optimally a pumped hydroelectric storage system. This technique relies on representing the system as a stochastic optimal control problem with state constraints, these latter corresponding to the finite volume of the reservoirs. Following the recent level-se…
Optimizes dividend policies in a Brownian model with controlled rates.
problem Realistic optimal dividend policies in a stochastic control problem.
method Delayed linear control strategies for refracted diffusion processes.
result Optimality of delayed linear control strategies for dividend payments.
The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.
The paper proposes a new stochastic intervention control model conducted in various commodity and stock markets. The essence of the phenomenon of intervention is described in accordance with current economic theory. A review of papers on intervention research has been made. A general construction of the stochastic inte…
Study uses DRL with Lagrangian relaxation to solve temporal control tasks with STL constraints.
problem Optimal control problems with temporal logic constraints.
method Extended CMDP formulation, Lagrangian relaxation, two-phase constrained DRL algorithm.
result Demonstrated learning performance of the proposed algorithm through simulations.
This work reviews left-invariant optimal control problems on Lie groups.
problem Optimal control problems on Lie groups with big symmetry.
method Review of main notions, methods, and results.
result Description of extremal trajectories and their optimality, cut time and cut locus, optimal synthesis.
We consider the exploration-exploitation tradeoff in linear quadratic (LQ) control problems, where the state dynamics is linear and the cost function is quadratic in states and controls. We analyze the regret of Thompson sampling (TS) (a.k.a. posterior-sampling for reinforcement learning) in the frequentist setting, i.…
Study uses viscosity solutions to solve control problems involving measure-valued martingales.
problem Stochastic control problems with measure-valued martingale state processes.
method Viscosity solution approach exploiting structural properties of MVM processes.
result Value function is the unique viscosity solution to the HJB equation.
We solve a complex Bayesian control problem with novel methods.
problem Optimizing control of a hidden signal's influence on noisy observations.
method Measure-valued HJB perspective, viscosity theory, approximation arguments.
result Equivalence to HJB equation and continuous viscosity solution.
In this paper we propose a new methodology for solving an uncertain stochastic Markovian control problem in discrete time. We call the proposed methodology the adaptive robust control. We demonstrate that the uncertain control problem under consideration can be solved in terms of associated adaptive robust Bellman equa…
Nonparametric adaptive robust control tackles model uncertainty in stochastic processes.
problem Model uncertainty in stochastic processes.
method Adaptive robust control methodology using online learning and uncertainty reduction, empirical distribution, and Lagrangian duality.
result Nonparametric adaptive robust control approach is preferable to traditional robust frameworks.
Efficient deep policy gradient method for continuous-time control problems.
problem Optimal control in continuous time with fine time discretization.
method Multi-scale deep policy gradient method with varying time discretization.
result Targeted efficiency in computational resources achieved through multi-scale approach.
New method solves stochastic control problems with delays using deep learning.
problem Stochastic control problems with delayed control in drift and diffusion.
method Characterization via Riccati PDEs and deep learning scheme.
result Illustrates effect of delay on Markowitz portfolio allocation problem.
In this paper, we adapt stochastic Perron's method to analyze a stochastic target problem with unbounded controls in a jump diffusion set-up. With this method, we construct a viscosity sub-solution and super-solution to the associated Hamiltonian-Jacobi-Bellman (HJB) equations. Under comparison principles, uniqueness o…
The paper tackles robust control with uncertain dependence using data-driven methods.
problem Nonparametric robust control under dependence uncertainty in multi-period stochastic systems.
method Nonparametric adaptive robust control framework using stochastic gradient descent ascent algorithm.
result The controller benefits from knowing more about the uncertain model.
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.