arXiv subjects

Helin Zhu

Publications and source records attributed to Helin Zhu.

8 recordsLinked to original sources

arXiv2026

Dynamic Whole-Body Dancing with Humanoid Robots -- A Model-Based Control Approach

This paper presents an integrated model-based framework for generating and executing dynamic whole-body dance motions on humanoid robots. The framework operates in two stages: offline motion generation and online motion execution, both leveraging future state prediction to enable robust and dynamic dance motions in real-world environments. In the offline motion generation stage, human dance demonstrations are captured via a motion capture (MoCap) system, retargeted to the robot by solving a Quadratic Programming (QP) problem, and further refined using Trajectory Optimization (TO) to ensure dynamic feasibility. In the online motion execution stage, a centroidal dynamics-based Model Predictive Control (MPC) framework tracks the planned motions in real time and proactively adjusts swing foot placement to adapt to real world disturbances. We validate our framework on the full-size humanoid robot Kuavo 4Pro, demonstrating the dynamic dance motions both in simulation and in a four-minute live public performance with a team of four robots. Experimental results show that longer prediction horizons improve both motion expressiveness in planning and stability in execution.

cs.RO↗

arXiv2017

Risk Quantification in Stochastic Simulation under Input Uncertainty

When simulating a complex stochastic system, the behavior of output response depends on input parameters estimated from finite real-world data, and the finiteness of data brings input uncertainty into the system. The quantification of the impact of input uncertainty on output response has been extensively studied. Most of the existing literature focuses on providing inferences on the mean response at the true but unknown input parameter, including point estimation and confidence interval construction. Risk quantification of mean response under input uncertainty often plays an important role in system evaluation and control, because it provides inferences on extreme scenarios of mean response in all possible input models. To the best of our knowledge, it has rarely been systematically studied in the literature. In this paper, first we introduce risk measures of mean response under input uncertainty, and propose a nested Monte Carlo simulation approach to estimate them. Then we develop asymptotical properties such as consistency and asymptotic normality for the proposed nested risk estimators. We further study the associated budget allocation problem for efficient nested risk simulation, and finally use a sharing economy example to illustrate the importance of accessing and controlling risk due to input uncertainty.

q-fin.RM↗

arXiv2017

A Bayesian Risk Approach to Data-driven Stochastic Optimization: Formulations and Asymptotics

A large class of stochastic programs involve optimizing an expectation taken with respect to an underlying distribution that is unknown in practice. One popular approach to addressing the distributional uncertainty, known as the distributionally robust optimization (DRO), is to hedge against the worst case over an uncertainty set of candidate distributions. However, it has been observed that inappropriate construction of the uncertainty set can sometimes result in over-conservative solutions. To explore the middle ground between optimistically ignoring the distributional uncertainty and pessimistically fixating on the worst-case scenario, we propose a Bayesian risk optimization (BRO) framework for parametric underlying distributions, which is to optimize a risk functional applied to the posterior distribution of an unknown distribution parameter. Of our particular interest are four risk functionals: mean, mean-variance, value-at-risk, and conditional value-at-risk. To unravel the implication of BRO, we establish the consistency of objective functions and optimal solutions, as well as the asymptotic normality of objective functions and optimal values. More importantly, our analysis reveals a hidden interpretation: the objectives of BRO can be approximately viewed as a weighted sum of posterior mean objective and the (squared) half-width of the true objective's confidence interval.

math.OC↗

arXiv2016

Solving Multi-Objective Optimization via Adaptive Stochastic Search with Domination Measure

For general multi-objective optimization problems, we propose a novel performance metric called domination measure to measure the quality of a solution, which can be intuitively interpreted as the size of the portion of the solution space that dominates that solution. As a result, we reformulate the original multi-objective problem into a stochastic single-objective one and propose a model-based approach to solve it. We show that an ideal version algorithm of the proposed approach converges to a set representation of the global optima of the reformulated problem. We also investigate the numerical performance of an implementable version algorithm by comparing it with numerous existing multi-objective optimization methods on popular benchmark test functions. The numerical results show that the proposed approach is effective in generating a finite and uniformly spread approximation of the Pareto optimal set of the original multi-objective problem, and is competitive to the tested existing methods.

math.OC↗

arXiv2016

Solving the Dual Problems of Dynamic Programs via Regression

In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the optimal value function. Theoretically, with the so called value-based optimal dual penalty, the optimal value function could be recovered exactly via strong duality. However, in practice, obtaining tight dual bounds usually requires good approximations of the optimal dual penalty, which could be time-consuming due to the conditional expectations that need to be estimated via nested simulation. In this paper, we will develop a framework of regression approach to approximating the optimal dual penalty in a non-nested manner, by exploring the structure of the function space consisting of all feasible dual penalties. The resulted approximations maintain to be feasible dual penalties, and thus yield valid dual bounds on the optimal value function. We show that the proposed framework is computationally efficient, and the resulted dual penalties lead to numerically tractable dual problems. Finally, we apply the framework to a high-dimensional dynamic trading problem to demonstrate its effectiveness in solving the dual problems of complex dynamic programs.

math.OC↗

arXiv2016

Simulation Optimization of Risk Measures with Adaptive Risk Levels

Optimizing risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) of a general loss distribution is usually difficult, because 1) the loss function might lack structural properties such as convexity or differentiability since it is often generated via black-box simulation of a stochastic system; 2) evaluation of risk measures often requires rare-event simulation, which is computationally expensive. In this paper, we study the extension of the recently proposed gradient-based adaptive stochastic search (GASS) to the optimization of risk measures VaR and CVaR. Instead of optimizing VaR or CVaR at the target risk level directly, we incorporate an adaptive updating scheme on the risk level, by initializing the algorithm at a small risk level and adaptively increasing it until the target risk level is achieved while the algorithm converges at the same time. This enables us to adaptively reduce the number of samples required to estimate the risk measure at each iteration, and thus improving the overall efficiency of the algorithm.

math.OC↗

arXiv2014

Weakly Coupled Dynamic Program: Information and Lagrangian Relaxations

"Weakly coupled dynamic program" describes a broad class of stochastic optimization problems in which multiple controlled stochastic processes evolve independently but subject to a set of linking constraints imposed on the controls. One feature of the weakly coupled dynamic program is that it decouples into lower-dimensional dynamic programs by dualizing the linking constraint via the Lagrangian relaxation, which also yields a bound on the optimal value of the original dynamic program. Together with the Lagrangian bound, we utilize the information relaxation approach that relaxes the non-anticipative constraint on the controls to obtain a tighter dual bound. We also investigate other combinations of the relaxations and place the resulting bounds in order. To tackle large-scale problems, we further propose a computationally tractable method based on information relaxation, and provide insightful interpretation and performance guarantee. We implement our method and demonstrate its use through two numerical examples.

math.OC↗

arXiv2013

Fast Estimation of True Bounds on Bermudan Option Prices under Jump-diffusion Processes

Fast pricing of American-style options has been a difficult problem since it was first introduced to financial markets in 1970s, especially when the underlying stocks' prices follow some jump-diffusion processes. In this paper, we propose a new algorithm to generate tight upper bounds on the Bermudan option price without nested simulation, under the jump-diffusion setting. By exploiting the martingale representation theorem for jump processes on the dual martingale, we are able to explore the unique structure of the optimal dual martingale and construct an approximation that preserves the martingale property. The resulting upper bound estimator avoids the nested Monte Carlo simulation suffered by the original primal-dual algorithm, therefore significantly improves the computational efficiency. Theoretical analysis is provided to guarantee the quality of the martingale approximation. Numerical experiments are conducted to verify the efficiency of our proposed algorithm.

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