arXiv subjects

Zhiping Chen

Publications and source records attributed to Zhiping Chen.

14 recordsLinked to original sources

arXiv2026

Adaptive Distributionally Robust Optimal Control with Bayesian Ambiguity Sets

In stochastic optimal control (SOC), uncertainty may arise from incomplete knowledge of the true probability distribution of the underlying environment, which is known as Knightian or epistemic uncertainty. Distributionally robust optimal control (DROC) models are subsequently proposed to tackle this source of uncertainty. While such models are effective in some practical applications, most existing DROC models are offline and can be overly conservative when data are scarce. Moreover, they cannot be applied to the case when samples are generated episodically. Motivated by the Bayesian SOC framework recently proposed by Shapiro et al.~\cite{shapiro2025episodic}, we propose an adaptive DROC model in which the ambiguity set is updated via Bayesian learning from new data. Under some moderate conditions, we derive a tractable risk-averse reformulation, establish consistency of the optimal value function and optimal policy for an infinite-horizon SOC and establish a finite-sample posterior credibility guarantee for the policy value induced by the proposed episodic Bayesian DROC model. We also study the stability and statistical robustness of the proposed model with respect to sample perturbations that often arise in data-driven environments. To solve the episodic Bayesian DROC model, we propose a Bellman-operator cutting-plane (BOCP) algorithm that is computationally efficient and provably convergent. Numerical results on an inventory control problem demonstrate the effectiveness, adaptivity, and robust performance of the proposed model and algorithm.

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arXiv2025

Stability Analysis of an Integrated Multistage Stochastic Programming and Markov Decision Process Problem

In this paper, we consider an integrated MSP-MDP framework which captures features of Markov decision process (MDP) and multistage stochastic programming (MSP). The integrated framework allows one to study a dynamic decision-making process that involves both transition of system states and dynamic change of the stochastic environment affected respectively by potential endogenous uncertainties and exogenous uncertainties. The integrated model differs from classical MDP models by taking into account the effect of history-dependent exogenous uncertainty and distinguishes itself from standard MSP models by explicitly considering transition of states between stages. We begin by deriving dynamic nested reformulation of the problem and the Lipschitz continuity and convexity of the stage-wise optimal value functions. We then move on to investigate stability of the problem in terms of the optimal value and the set of optimal solutions under the perturbations of the probability distributions of the endogenous uncertainty and the exogenous uncertainty. Specifically, we quantify the effects of the perturbation of the two uncertainties on the optimal values and optimal solutions by deriving the error bounds in terms of Kantorovich metric and Fortet-Mourier metric of the probability distributions of the respective uncertainties. These results differ from the existing stability results established in terms of the filtration distance \cite{heitsch2009scenario} or the nested distance \cite{pflug2012distance}. We use some examples to explain the differences via tightness of the error bounds and applicability of the stability results. The results complement the existing stability results and provide new theoretical grounding for emerging integrated MSP-MDP models.

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arXiv2025

Bayesian distributionally robust variational inequalities: regularization and quantification

We propose a Bayesian distributionally robust variational inequality (DRVI) framework that models the data-generating distribution through a finite mixture family, which allows us to study the DRVI on a tractable finite-dimensional parametric ambiguity set. To address distributional uncertainty, we construct a data-driven ambiguity set with posterior coverage guarantees via Bayesian inference. We also employ a regularization approach to ensure numerical stability. We prove the existence of solutions to the Bayesian DRVI and the asymptotic convergence to a solution as sample size grows to infinity and the regularization parameter goes to zero. Moreover, we derive quantitative stability bounds and finite-sample guarantees under data scarcity and contamination. Numerical experiments on a distributionally robust multi-portfolio Nash equilibrium problem validate our theoretical results and demonstrate the robustness and reliability of Bayesian DRVI solutions in practice.

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arXiv2025

A Bayesian Composite Risk Approach for Stochastic Optimal Control and Markov Decision Processes

Inspired by Shapiro et al.~\cite{shapiro2023episodic}, we consider a stochastic optimal control (SOC) and Markov decision process (MDP) where the risks arising from epistemic and aleatoric uncertainties are assessed using Bayesian composite risk (BCR) measures (Qian et al.~\cite{qian2019composite}). The time dependence of the risk measures allows us to capture the decision maker's (DM) dynamic risk preferences opportunely as increasing information about both uncertainties is obtained. This makes the new BCR-SOC/MDP model more flexible than conventional risk-averse SOC/MDP models. Unlike \cite{shapiro2023episodic} where the control/action at each episode is based on the current state alone, the new model allows the control to depend on the probability distribution of the epistemic uncertainty, which reflects the fact that in many practical instances the cumulative information about epistemic uncertainty often affects the DM's belief about the future aleatoric uncertainty and hence the DM's action \cite{strens2000bayesian}. The new modeling paradigm incorporates several existing SOC/MDP models including distributionally robust SOC/MDP models and Bayes-adaptive MDP models and generates so-called preference robust SOC/MDP models. Moreover, we derive conditions under which the BCR-SOC/MDP model is well-defined, demonstrate that finite-horizon BCR-SOC/MDP models can be solved using dynamic programming techniques, and extend the discussion to the infinite-horizon case. By using Bellman equations, we show that under some standard conditions, asymptotic convergence of the optimal values and optimal actions as the episodic variable goes to infinity is achieved. Finally, we carry out numerical tests on a finite horizon spread betting problem and an inventory control problem and show the effectiveness of the proposed model and numerical schemes.

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arXiv2025

Meta-Learning the Optimal Mixture of Strategies for Online Portfolio Selection

This paper presents an innovative online portfolio selection model, situated within a meta-learning framework, that leverages a mixture policies strategy. The core idea is to simulate a fund that employs multiple fund managers, each skilled in handling different market environments, and dynamically allocate our funding to these fund managers for investment. To address the non-stationary nature of financial markets, we divide the long-term process into multiple short-term processes to adapt to changing environments. We use a clustering method to identify a set of historically high-performing policies, characterized by low similarity, as candidate policies. Additionally, we employ a meta-learning method to search for initial parameters that can quickly adapt to upcoming target investment tasks, effectively providing a set of well-suited initial strategies. Subsequently, we update the initial parameters using the target tasks and determine the optimal mixture weights for these candidate policies. Empirical tests show that our algorithm excels in terms of training time and data requirements, making it particularly suitable for high-frequency algorithmic trading. To validate the effectiveness of our method, we conduct numerical tests on cross-training datasets, demonstrating its excellent transferability and robustness.

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arXiv2024

Learning complexity of gradient descent and conjugate gradient algorithms

Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed to minimize cost functions. In these algorithms, tunable parameters, such as step sizes or conjugate parameters, play a crucial role in determining key performance metrics, like runtime and solution quality. In this work, we introduce a framework that models algorithm selection as a statistical learning problem, and thus learning complexity can be estimated by the pseudo-dimension of the algorithm group. We first propose a new cost measure for unconstrained optimization algorithms, inspired by the concept of primal-dual integral in mixed-integer linear programming. Based on the new cost measure, we derive an improved upper bound for the pseudo-dimension of gradient descent algorithm group by discretizing the set of step size configurations. Moreover, we generalize our findings from gradient descent algorithm to the conjugate gradient algorithm group for the first time, and prove the existence a learning algorithm capable of probabilistically identifying the optimal algorithm with a sufficiently large sample size.

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arXiv2024

A dynamical neural network approach for distributionally robust chance constrained Markov decision process

In this paper, we study the distributionally robust joint chance constrained Markov decision process. {Utilizing the logarithmic transformation technique,} we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set. To cope with the non-convexity and improve the robustness of the solution, we propose a dynamical neural network approach to solve the reformulated optimization problem. Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.

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arXiv2023

Data-driven Approximation of Distributionally Robust Chance Constraints using Bayesian Credible Intervals

The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the distributionally robust chance constraint is satisfied with high probability. To incorporate available data and prior distribution knowledge, we construct ambiguity sets for the distributionally robust chance constraint using Bayesian credible intervals. We establish the congruent relationship between the ambiguity set in Bayesian distributionally robust chance constraints and the uncertainty set in a specific robust optimization. In contrast to most existent uncertainty set construction methods which are only applicable for particular settings, our approach provides a unified framework for constructing uncertainty sets under different marginal distribution assumptions, thus making it more flexible and widely applicable. Additionally, under the concavity assumption, our method provides strong finite sample probability guarantees for optimal solutions. The practicality and effectiveness of our approach are illustrated with numerical experiments on portfolio management and queuing system problems. Overall, our approach offers a promising solution to distributionally robust chance constrained problems and has potential applications in other fields.

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arXiv2023

Multistage Utility Preference Robust Optimization

In this paper, we consider a multistage expected utility maximization problem where the decision maker's utility function at each stage depends on historical data and the information on the true utility function is incomplete. To mitigate adverse impact arising from ambiguity of the true utility, we propose a maximin robust model where the optimal policy is based on the worst-case sequence of utility functions from an ambiguity set constructed with partially available information about the decision maker's preferences. We then show that the multistage maximin problem is time consistent when the utility functions are state-dependent and demonstrate with a counter example that the time consistency may not be retained when the utility functions are state-independent. With the time consistency, we show the maximin problem can be solved by a recursive formula whereby a one-stage maximin problem is solved at each stage beginning from the last stage. Moreover, we propose two approaches to construct the ambiguity set: a pairwise comparison approach and a zeta-ball approach where a ball of utility functions centered at a nominal utility function under zeta-metric is considered. To overcome the difficulty arising from solving the infinite dimensional optimization problem in computation of the worst-case expected utility value, we propose piecewise linear approximation of the utility functions and derive error bound for the approximation under moderate conditions. Finally, we use the SDDP method and the nested Benders' decomposition method to solve the multistage state-dependent preference robust problem and the scenario tree method to solve the state-independent problem, and carry out comparative analysis on the efficiency of the computational schemes as well as out-of-sample performances of the state-dependent and state-independent models.

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arXiv2021

Distributionally robust second-order stochastic dominance constrained optimization with Wasserstein ball

We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the empirical distribution. We adopt the sample approximation approach to develop a linear programming formulation that provides a lower bound. We propose a novel split-and-dual decomposition framework which provides an upper bound. We establish quantitative convergency for both lower and upper approximations given some constraint qualification conditions. To efficiently solve the non-convex upper bound problem, we use a sequential convex approximation algorithm. Numerical evidences on a portfolio selection problem valid the convergency and effectiveness of the proposed two approximation methods.

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arXiv2021

The Tianlai Dish Pathfinder Array: design, operation and performance of a prototype transit radio interferometer

The Tianlai Dish Pathfinder Array is a radio interferometer designed to test techniques for 21~cm intensity mapping in the post-reionization universe as a means for measuring large-scale cosmic structure. It performs drift scans of the sky at constant declination. We describe the design, calibration, noise level, and stability of this instrument based on the analysis of about $\sim 5 \%$ of 6,200 hours of on-sky observations through October, 2019. Beam pattern determinations using drones and the transit of bright sources are in good agreement, and compatible with electromagnetic simulations. Combining all the baselines, we make maps around bright sources and show that the array behaves as expected. A few hundred hours of observations at different declinations have been used to study the array geometry and pointing imperfections, as well as the instrument noise behaviour. We show that the system temperature is below 80~K for most feed antennas, and that noise fluctuations decrease as expected with integration time, at least up to a few hundred seconds. Analysis of long integrations, from 10 nights of observations of the North Celestial Pole, yielded visibilities with amplitudes of 20-30~mK, consistent with the expected signal from the NCP radio sky with $<10\,$mK precision for $1 ~\mathrm{MHz} \times 1~ \mathrm{min}$ binning. Hi-pass filtering the spectra to remove smooth spectrum signal yields a residual consistent with zero signal at the $0.5\,$mK level.

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arXiv2018

Progress in the Construction and Testing of the Tianlai Radio Interferometers

The Tianlai Pathfinder is designed to demonstrate the feasibility of using a wide field of view radio interferometers to map the density of neutral hydrogen in the Universe after the Epoch of Reionizaton. This approach, called 21~cm intensity-mapping, promises an inexpensive means for surveying the large-scale structure of the cosmos. The Tianlai Pathfinder presently consists of an array of three, 15~m $\times$ 40~m cylinder telescopes and an array of sixteen, 6~m diameter dish antennas located in a radio-quiet part of western China. The two types of arrays were chosen to determine the advantages and disadvantages of each approach. The primary goal of the Pathfinder is to make 3D maps by surveying neutral hydrogen over large areas of the sky %$20,000 {\rm deg}^2$ in two different redshift ranges: first at $1.03 > z > 0.78$ ($700 - 800$~MHz) and later at $0.21 > z > 0.12$ ($1170 - 1270$~MHz). The most significant challenge to $21$~cm intensity-mapping is the removal of strong foreground radiation that dwarfs the cosmological signal. It requires exquisite knowledge of the instrumental response, i.e. calibration. In this paper, we provide an overview of the status of the Pathfinder and discuss the details of some of the analysis that we have carried out to measure the beam function of both arrays. We compare electromagnetic simulations of the arrays to measurements, discuss measurements of the gain and phase stability of the instrument, and provide a brief overview of the data processing pipeline.

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arXiv2017

Simulation and Testing of a Linear Array of Modified Four-Square Feed Antennas for the Tianlai Cylindrical Radio Telescope

A wide bandwidth, dual polarized, modified four-square antenna is presented as a feed antenna for radio astronomical measurements. A linear array of these antennas is used as a line-feed for cylindrical reflectors for Tianlai, a radio interferometer designed for 21~cm intensity mapping. Simulations of the feed antenna beam patterns and scattering parameters are compared to experimental results at multiple frequencies across the 650 - 1420 MHz range. Simulations of the beam patterns of the combined feed array/reflector are presented as well.

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arXiv2010

MARVELS-1b: A Short-Period, Brown Dwarf Desert Candidate from the SDSS-III MARVELS Planet Search

We present a new short-period brown dwarf candidate around the star TYC 1240-00945-1. This candidate was discovered in the first year of the Multi-object APO Radial Velocity Exoplanets Large-area Survey (MARVELS), which is part of the third phase of the Sloan Digital Sky Survey (SDSS-III), and we designate the brown dwarf as MARVELS-1b. MARVELS uses the technique of dispersed fixed-delay interferometery to simultaneously obtain radial velocity measurements for 60 objects per field using a single, custom-built instrument that is fiber fed from the SDSS 2.5-m telescope. From our 20 radial velocity measurements spread over a ~370 d time baseline, we derive a Keplerian orbital fit with semi-amplitude K=2.533+/-0.025 km/s, period P=5.8953+/-0.0004 d, and eccentricity consistent with circular. Independent follow-up radial velocity data confirm the orbit. Adopting a mass of 1.37+/-0.11 M_Sun for the slightly evolved F9 host star, we infer that the companion has a minimum mass of 28.0+/-1.5 M_Jup, a semimajor axis 0.071+/-0.002 AU assuming an edge-on orbit, and is probably tidally synchronized. We find no evidence for coherent instrinsic variability of the host star at the period of the companion at levels greater than a few millimagnitudes. The companion has an a priori transit probability of ~14%. Although we find no evidence for transits, we cannot definitively rule them out for companion radii ~<1 R_Jup.

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