Combines Gaussian processes and polynomial chaos for stochastic control.
problem Uncertainties in dynamic models lead to performance issues in predictive control.
method Combines Gaussian processes with polynomial chaos expansions to estimate probability distributions of nonlinear functions.
result Demonstrates accurate approximation and closed-loop performance in stochastic nonlinear model predictive control.
A new approach optimizes weights in DLP for better risk-adjusted performance.
problem Optimizing time-varying weights in Double Linear Policy (DLP) for better risk-adjusted performance.
method Stochastic Model Predictive Control (SMPC) framework to maximize risk-adjusted returns while enforcing constraints.
result Empirical results show improved risk-adjusted performance and drawdown control.
Bayesian optimisation tackles stochastic MPC hyper-parameter tuning.
problem Fine-tuning hyper-parameters in stochastic MPC models.
method Heteroscedastic Bayesian optimisation framework.
result Framework effectively tunes hyper-parameters in control problems.
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…
We seek a discussion about the most suitable feedback control structure for stock trading under the consideration of proportional transaction costs. Suitability refers to robustness and performance capability. Both are tested by considering different one-step ahead prediction qualities, including the ideal case, correc…
Method predicts hardware resource usage by control software with guaranteed linear convergence.
problem Predicting time-varying hardware resource availability in control software.
method Path structured multimarginal Schrödinger bridge (MSBP) for learning stochastic resource usage.
result Guaranteed linear convergence to accurate prediction of hardware resource utilization.
Paper uses machine learning and SIR models to predict COVID-19 cases.
problem Predicting the spread of COVID-19 cases for control measures.
method Machine learning and SIR models (deterministic and stochastic) with numerical approximations.
result Predictions help in finding concrete actions to control the pandemic.
MPC outperforms reactive budgeting in non-stationary return environments.
problem Optimizing budget allocation under non-stationary returns.
method Receding-horizon Model Predictive Control (MPC) compared to reactive policies.
result MPC consistently outperforms reactive budgeting when return dynamics are predictable.
Foundational brain dynamics model using stochastic optimal control.
problem Complex and noisy fMRI signals in brain dynamics.
method Continuous-discrete state space model with amortized inference and locally linear approximations.
result State-of-the-art results across various downstream tasks.
NeuralChaos efficiently approximates complex stochastic processes.
problem Representing and computing square-integrable predictable processes over time.
method Introduces NeuralChaos, a neural operator architecture for Rd-valued predictable processes. result NeuralChaos achieves best N-term chaoslet approximation rates and is dense in HT2(Rd). BCI provides calibrated prediction intervals for time series forecasts.
problem Calibration of prediction intervals for time series forecasts.
method BCI wraps around any time series forecasting models and optimizes interval lengths using dynamic programming.
result BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence.
Solves Merton's investment-consumption problem with certainty equivalent approach.
problem Maximizing CRRA utility of consumption over time and investment mix.
method Identifies a certainty equivalent problem for the Merton problem, reformulates it as an SOCP, and applies it to model predictive control.
result The certainty equivalent problem can be solved as an SOCP, facilitating model predictive control.
We propose directed time series regression, a new approach to estimating parameters of time-series models for use in certainty equivalent model predictive control. The approach combines merits of least squares regression and empirical optimization. Through a computational study involving a stochastic version of a well …
This work proposes an online learning approach to tighten constraints in stochastic control problems.
problem Solving chance-constrained stochastic optimal control problems is computationally challenging.
method Reformulate chance constraints as a binary regression problem and use a GP model to learn constraint-tightening parameters online.
result The approach tightens constraints more effectively, leading to lower costs in numerical experiments.
Safe learning of stochastic dynamics with safety constraints.
problem Learning controlled stochastic dynamics with safety constraints.
method Iterative expansion of a safe control set using kernel-based confidence bounds.
result The method ensures safe exploration and efficient estimation of system dynamics.
Itô maps provide a method for any-step SDE integration.
problem Stochastic dynamics
method Itô map formulation
result Empirical results on synthetic and image-generation benchmarks
Optimizes control of infectious disease spread using stochastic methods.
problem Optimizing control of highly infectious diseases like COVID-19.
method Reformulated Hamilton-Jacobi-Bellman equation as stochastic minimum principle, leading to forward-backward stochastic differential equations.
result Numerous numerical solutions presented under various scenarios.
NOVAS uses adaptive stochastic search for non-convex optimization in deep networks.
problem Non-convex optimization challenges in deep neural networks.
method Adaptive stochastic search for non-convex optimization.
result NOVAS outperforms existing alternatives in a structured prediction task.
Study risk-controlling prediction sets for single trajectory data from dynamical systems.
problem Performance guarantees for risk-controlling prediction sets in single trajectory data from unknown stochastic dynamical systems.
method Used blocking and decoupling techniques to analyze performance guarantees under different data generating processes.
result Performance guarantees similar to iid setting when data is stationary and contractive, with graceful degradation otherwise.
A new method calibrates scientific models by adding randomness to their predictions.
problem Current scientific foundation models lack calibrated uncertainty.
method Stochastic Attention, which randomizes attention weights using multinomial samples.
result Stochastic Attention achieves the strongest native calibration and sharpest prediction intervals.
Novel method estimates complex nonlinear systems with stochastic differential equations.
problem Handling complex nonlinear dynamical systems with strong learning guarantees.
method Estimates drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled stochastic differential equations.
result Strong theoretical guarantees including finite-sample bounds for various metrics.
One of the challenges in model-based control of stochastic dynamical systems is that the state transition dynamics are involved, and it is not easy or efficient to make good-quality predictions of the states. Moreover, there are not many representational models for the majority of autonomous systems, as it is not easy …
We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the relationship between different types of stochastic gradient algorithms. We show the conver…
Proposes a recursive MPC scheme with probabilistic safety guarantees for uncertain dynamic systems.
problem Probabilistic safety guarantees for MPC in dynamic environments with unknown stochastic agents.
method Uses conformal prediction to derive high-confidence prediction regions and gradually relax safety constraints online.
result Ensures recursive feasibility of MPC schemes by relaxing safety constraints over time.
This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using tools from stochastic control, and how to rigorously verify their optimality by mea…
Log-ergodic model improves velocity of money prediction.
problem Improving velocity of money prediction for economic control.
method Log-ergodic processes to simulate monetary velocity.
result Log-ergodic model offers superior predictive power.
This paper explains CART random forests using stochastic control theory.
problem Understanding the inner workings of CART random forests.
method Developed a stochastic-control perspective on CART random forests, interpreting feature subsampling as a random feasible action set and the split rule as a policy.
result Established that the CART policy is locally stabilizing but globally suboptimal for the forest objective.
Optimal market making improves liquidity in prediction markets.
problem Efficient price discovery in prediction markets.
method Stochastic control framework for optimal market making.
result Optimal market quotes improve downside protection and profit.
Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this context the model must be able to capture the multi-modal nature of the data, w…
New PFPPs based on rank-dependent utility for better performance control.
problem Improving performance prediction in systems with short-term control.
method Introduces rank-dependent PFPPs, solves integral equations via Volterra theory.
result Existence of rank-dependent PFPPs under specific market conditions.
Continuous reinforcement learning such as DDPG and A3C are widely used in robot control and autonomous driving. However, both methods have theoretical weaknesses. While DDPG cannot control noises in the control process, A3C does not satisfy the continuity conditions under the Gaussian policy. To address these concerns,…
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.
We study data poisoning attacks in the online setting where training items arrive sequentially, and the attacker may perturb the current item to manipulate online learning. Importantly, the attacker has no knowledge of future training items nor the data generating distribution. We formulate online data poisoning attack…
New algorithm borrows future randomness to stabilize model-free control.
problem Double sampling problem in model-free control with nonlinear approximations.
method Borrowing from the future (BFF) algorithm to approximate re-sampling of next states.
result BFF is close to unbiased SGD under smooth dynamics, validated by simulations.
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.
Method learns software resource usage from snapshots.
problem Challenges in learning time-varying, correlated resource usage.
method Graph structured Schrödinger bridge problem for nonparametric learning.
result Predicts most-likely resource distributions.
New approach solves utility maximization problems using Delta family.
problem Utility maximization in stochastic control problems.
method Directly solving DP equation with Delta function representation.
result Explicit series representation of value function.
Deep learning solves complex stochastic control with jumps.
problem Solving high-dimensional stochastic control tasks with jumps.
method Model-based approach using two neural networks, iteratively trained with objectives derived from the Hamilton-Jacobi-Bellman equation.
result Demonstrates effectiveness in solving complex high-dimensional stochastic control tasks.
We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process X(t) and a \emph{predictive mean-field} backward SDE (BSDE) in the unknowns Y(t),Z(t),K(t,⋅). The driver of …
This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The resulting latent force models (LFMs) can be seen as hybrid models that contain a first…
A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic control problems as analytical solutions are not tractable in general. This paper ge…
New method tackles model uncertainty in stochastic control using Bayesian nonparametrics.
problem Model uncertainty in stochastic control problems.
method Nonparametric Bayesian approach with Dirichlet process for unknown distributions, online learning, and Gaussian process surrogates.
result Demonstrates financial advantages of nonparametric Bayesian over parametric methods.
Study cost-driven state representation learning for control from partial observations.
problem Learning state representation for control from partial and high-dimensional observations.
method Cost-driven state representation learning via predicting cumulative costs.
result Established finite-sample guarantees for near-optimal representation and controller.
A new method for stochastic optimal control improves accuracy over existing techniques.
problem Improving the accuracy of stochastic optimal control for noisy systems.
method Stochastic Optimal Control Matching (SOCM) using Iterative Diffusion Optimization (IDO) with path-wise reparameterization trick.
result SOCM achieves lower error than existing techniques for three out of four control problems, sometimes by an order of magnitude.
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.
We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfu…
Develops a model for bid and ask prices using stochastic control.
problem Modeling bid and ask prices of a European asset.
method Formulates a stochastic control problem, uses Girsanov theorem, Esscher transform, and dynamic programming.
result Derives equations to determine bid and ask prices.
RL applied to TCLs for power consumption control.
problem Optimizing power consumption using TCLs with RL.
method Modelica-based reinforcement learning (Q-learning) for stochastic TCLs.
result Q-learning parameters affect controller performance.