On Parametric Optimal Execution and Machine Learning Surrogates

• URL: http://arxiv.org/abs/2204.08581v3
• Date: Sun, 29 Oct 2023 07:08:03 GMT
• Title: On Parametric Optimal Execution and Machine Learning Surrogates
• Authors: Tao Chen and Mike Ludkovski and Moritz Vo{\ss}
• Abstract summary: We investigate optimal order execution problems in discrete time with instantaneous price impact and resilience. We develop a numerical algorithm based on dynamic programming and deep learning.
• Score: 3.077531983369872
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate optimal order execution problems in discrete time with instantaneous price impact and stochastic resilience. First, in the setting of linear transient price impact we derive a closed-form recursion for the optimal strategy, extending the deterministic results from Obizhaeva and Wang (J Financial Markets, 2013). Second, we develop a numerical algorithm based on dynamic programming and deep learning for the case of nonlinear transient price impact as proposed by Bouchaud et al. (Quant. Finance, 2004). Specifically, we utilize an actor-critic framework that constructs two neural-network (NN) surrogates for the value function and the feedback control. The flexible scalability of NN functional approximators enables parametric learning, i.e., incorporating several model or market parameters as part of the input space. Precise calibration of price impact, resilience, etc., is known to be extremely challenging and hence it is critical to understand sensitivity of the execution policy to these parameters. Our NN learner organically scales across multiple input dimensions and is shown to accurately approximate optimal strategies across a wide range of parameter configurations. We provide a fully reproducible Jupyter Notebook with our NN implementation, which is of independent pedagogical interest, demonstrating the ease of use of NN surrogates in (parametric) stochastic control problems.

Related papers

• A Stochastic Approach to Bi-Level Optimization for Hyperparameter Optimization and Meta Learning [74.80956524812714]
  We tackle the general differentiable meta learning problem that is ubiquitous in modern deep learning. These problems are often formalized as Bi-Level optimizations (BLO) We introduce a novel perspective by turning a given BLO problem into a ii optimization, where the inner loss function becomes a smooth distribution, and the outer loss becomes an expected loss over the inner distribution.
  arXiv  Detail & Related papers  (2024-10-14T12:10:06Z)
• Stochastic Q-learning for Large Discrete Action Spaces [79.1700188160944]
  In complex environments with discrete action spaces, effective decision-making is critical in reinforcement learning (RL) We present value-based RL approaches which, as opposed to optimizing over the entire set of $n$ actions, only consider a variable set of actions, possibly as small as $mathcalO(log(n)$)$. The presented value-based RL methods include, among others, Q-learning, StochDQN, StochDDQN, all of which integrate this approach for both value-function updates and action selection.
  arXiv  Detail & Related papers  (2024-05-16T17:58:44Z)
• Active Learning with Fully Bayesian Neural Networks for Discontinuous and Nonstationary Data [0.0]
  We introduce fully Bayesian Neural Networks (FBNNs) for active learning tasks in the'small data' regime. FBNNs provide reliable predictive distributions, crucial for making informed decisions under uncertainty in the active learning setting. Here, we assess the suitability and performance of FBNNs with the No-U-Turn Sampler for active learning tasks in the'small data' regime.
  arXiv  Detail & Related papers  (2024-05-16T05:20:47Z)
• End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty [55.04219793298687]
  The Predict-Then-Forecast (PtO) paradigm in machine learning aims to maximize downstream decision quality. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives. It shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.
  arXiv  Detail & Related papers  (2024-02-12T16:33:35Z)
• Dynamically configured physics-informed neural network in topology optimization applications [4.403140515138818]
  The physics-informed neural network (PINN) can avoid generating enormous amounts of data when solving forward problems. A dynamically configured PINN-based topology optimization (DCPINN-TO) method is proposed. The accuracy of the displacement prediction and optimization results indicate that the DCPINN-TO method is effective and efficient.
  arXiv  Detail & Related papers  (2023-12-12T05:35:30Z)
• Fine-Tuning Adaptive Stochastic Optimizers: Determining the Optimal Hyperparameter $ε$ via Gradient Magnitude Histogram Analysis [0.7366405857677226]
  We introduce a new framework based on the empirical probability density function of the loss's magnitude, termed the "gradient magnitude histogram" We propose a novel algorithm using gradient magnitude histograms to automatically estimate a refined and accurate search space for the optimal safeguard.
  arXiv  Detail & Related papers  (2023-11-20T04:34:19Z)
• Sub-linear Regret in Adaptive Model Predictive Control [56.705978425244496]
  We present STT-MPC (Self-Tuning Tube-based Model Predictive Control), an online oracle that combines the certainty-equivalence principle and polytopic tubes. We analyze the regret of the algorithm, when compared to an algorithm initially aware of the system dynamics.
  arXiv  Detail & Related papers  (2023-10-07T15:07:10Z)
• Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processes [80.89852729380425]
  We propose the first computationally efficient algorithm that achieves the nearly minimax optimal regret $tilde O(dsqrtH3K)$. Our work provides a complete answer to optimal RL with linear MDPs, and the developed algorithm and theoretical tools may be of independent interest.
  arXiv  Detail & Related papers  (2022-12-12T18:58:59Z)
• Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting [91.43582419264763]
  We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model.
  arXiv  Detail & Related papers  (2020-03-12T19:56:38Z)
• Online Parameter Estimation for Safety-Critical Systems with Gaussian Processes [6.122161391301866]
  We present a Bayesian optimization framework based on Gaussian processes (GPs) for online parameter estimation. It uses an efficient search strategy over a response surface in the parameter space for finding the global optima with minimal function evaluations. We demonstrate our technique on an actuated planar pendulum and safety-critical quadrotor in simulation with changing parameters.
  arXiv  Detail & Related papers  (2020-02-18T20:38:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.