arXiv subjects

Andrew Zheng

Publications and source records attributed to Andrew Zheng.

15 recordsLinked to original sources

arXiv2026

Generalized Adjoint Method

The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex variables, which occur often in many inverse problems in electromagnetism and signal processing problems, both the cost and constraint can become non-holomorphic and hence non-differentiable in the standard definitions. Using the notion of CR-calculus, a generalized adjoint method is introduced that can compute the direction of steepest ascent for the cost function while enforcing the constraint even if both are non-holomorphic.

math.OC↗

arXiv2025

Differences-in-Neighbors for Network Interference in Experiments

Experiments in online platforms frequently suffer from network interference, in which a treatment applied to a given unit affects outcomes for other units connected via the platform. This SUTVA violation biases naive approaches to experiment design and estimation. A common solution is to reduce interference by clustering connected units, and randomizing treatments at the cluster level, typically followed by estimation using one of two extremes: either a simple difference-in-means (DM) estimator, which ignores remaining interference; or an unbiased Horvitz-Thompson (HT) estimator, which eliminates interference at great cost in variance. Even combined with clustered designs, this presents a limited set of achievable bias variance tradeoffs. We propose a new estimator, dubbed Differences-in-Neighbors (DN), designed explicitly to mitigate network interference. Compared to DM estimators, DN achieves bias second order in the magnitude of the interference effect, while its variance is exponentially smaller than that of HT estimators. When combined with clustered designs, DN offers improved bias-variance tradeoffs not achievable by existing approaches. Empirical evaluations on a large-scale social network and a city-level ride-sharing simulator demonstrate the superior performance of DN in experiments at practical scale.

cs.SI↗

arXiv2025

Evaluating singular and near-singular integrals on $C^2$ smooth surfaces with quadratic geometric approximation and closed form expressions

Most Fredholm integral equations involve integrals with weakly singular kernels. Once the domain of integration is discretized into flat triangular elements, these weakly singular kernels become strongly singular or near-singular. Common methods to compute these integrals when the kernel is a Green's function include the Duffy transform, polar coordinates with closed analytic formulas, and singularity extraction. However, these methods do not generalize well to the normal derivatives of Green's functions due to the strongly singular behavior of these functions on triangular elements. We provide methods to integrate both the Green's function and its normal derivative on smooth surfaces discretized by triangular elements in three dimensions for many commonly encountered differential operators. For strongly singular integrals involving normal derivatives of Green's functions, we introduce a more refined approximation of the derivatives of the Green's function on flat triangles. This method uses geometric information of the true surface of integration to approximate the original integral on the true domain using push-forward maps. This is better than simply setting the singular integrals to zero, while being faster than adaptive refinement methods. We provide an algorithm for explicit computations on triangles, and present necessary analytic formulas that the algorithm requires in the appendix.

math.NA↗

arXiv2024

Speeding up Policy Simulation in Supply Chain RL

Simulating a single trajectory of a dynamical system under some state-dependent policy is a core bottleneck in policy optimization (PO) algorithms. The many inherently serial policy evaluations that must be performed in a single simulation constitute the bulk of this bottleneck. In applying PO to supply chain optimization (SCO) problems, simulating a single sample path corresponding to one month of a supply chain can take several hours. We present an iterative algorithm to accelerate policy simulation, dubbed Picard Iteration. This scheme carefully assigns policy evaluation tasks to independent processes. Within an iteration, any given process evaluates the policy only on its assigned tasks while assuming a certain "cached" evaluation for other tasks; the cache is updated at the end of the iteration. Implemented on GPUs, this scheme admits batched evaluation of the policy across a single trajectory. We prove that the structure afforded by many SCO problems allows convergence in a small number of iterations independent of the horizon. We demonstrate practical speedups of 400x on large-scale SCO problems even with a single GPU, and also demonstrate practical efficacy in other RL environments.

cs.AI↗

arXiv2024

Effects of Dataset Sampling Rate for Noise Cancellation through Deep Learning

Background: Active noise cancellation has been a subject of research for decades. Traditional techniques, like the Fast Fourier Transform, have limitations in certain scenarios. This research explores the use of deep neural networks (DNNs) as a superior alternative. Objective: The study aims to determine the effect sampling rate within training data has on lightweight, efficient DNNs that operate within the processing constraints of mobile devices. Methods: We chose the ConvTasNET network for its proven efficiency in speech separation and enhancement. ConvTasNET was trained on datasets such as WHAM!, LibriMix, and the MS-2023 DNS Challenge. The datasets were sampled at rates of 8kHz, 16kHz, and 48kHz to analyze the effect of sampling rate on noise cancellation efficiency and effectiveness. The model was tested on a core-i7 Intel processor from 2023, assessing the network's ability to produce clear audio while filtering out background noise. Results: Models trained at higher sampling rates (48kHz) provided much better evaluation metrics against Total Harmonic Distortion (THD) and Quality Prediction For Generative Neural Speech Codecs (WARP-Q) values, indicating improved audio quality. However, a trade-off was noted with the processing time being longer for higher sampling rates. Conclusions: The Conv-TasNET network, trained on datasets sampled at higher rates like 48kHz, offers a robust solution for mobile devices in achieving noise cancellation through speech separation and enhancement. Future work involves optimizing the model's efficiency further and testing on mobile devices.

cs.SD↗

arXiv2024

Synthesizing Controller for Safe Navigation using Control Density Function

We consider the problem of navigating a nonlinear dynamical system from some initial set to some target set while avoiding collision with an unsafe set. We extend the concept of density function to control density function (CDF) for solving navigation problems with safety constraints. The occupancy-based interpretation of the measure associated with the density function is instrumental in imposing the safety constraints. The navigation problem with safety constraints is formulated as a quadratic program (QP) using CDF. The existing approach using the control barrier function (CBF) also formulates the navigation problem with safety constraints as QP. One of the main advantages of the proposed QP using CDF compared to QP formulated using CBF is that both the convergence/stability and safety can be combined and imposed using the CDF. Simulation results involving the Duffing oscillator and safe navigation of Dubin car models are provided to verify the main findings of the paper.

eess.SY↗

arXiv2023

Safe Motion Planning for Quadruped Robots Using Density Functions

This paper presents a motion planning algorithm for quadruped locomotion based on density functions. We decompose the locomotion problem into a high-level density planner and a model predictive controller (MPC). Due to density functions having a physical interpretation through the notion of occupancy, it is intuitive to represent the environment with safety constraints. Hence, there is an ease of use to constructing the planning problem with density. The proposed method uses a simplified model of the robot into an integrator system, where the high-level plan is in a feedback form formulated through an analytically constructed density function. We then use the MPC to optimize the reference trajectory, in which a low-level PID controller is used to obtain the torque level control. The overall framework is implemented in simulation, demonstrating our feedback density planner for legged locomotion. The implementation of work is available at \url{https://github.com/AndrewZheng-1011/legged_planner}

cs.RO↗

arXiv2023

Optimal Control for Quadruped Locomotion using LTV MPC

This paper presents a state-of-the-art optimal controller for quadruped locomotion. The robot dynamics is represented using a single rigid body (SRB) model. A linear time-varying model predictive controller (LTV MPC) is proposed by using linearization schemes. Simulation results show that the LTV MPC can execute various gaits, such as trot and crawl, and is capable of tracking desired reference trajectories even under unknown external disturbances. The LTV MPC is implemented as a quadratic program using qpOASES through the CasADi interface at 50 Hz. The proposed MPC can reach up to 1 m/s top speed with an acceleration of 0.5 m/s2 executing a trot gait. The implementation is available at https:// github.com/AndrewZheng-1011/Quad_ConvexMPC

cs.RO↗

arXiv2023

Safe Navigation using Density Functions

This paper presents a novel approach for safe control synthesis using the dual formulation of the navigation problem. The main contribution of this paper is in the analytical construction of density functions for almost everywhere navigation with safety constraints. In contrast to the existing approaches, where density functions are used for the analysis of navigation problems, we use density functions for the synthesis of safe controllers. We provide convergence proof using the proposed density functions for navigation with safety. Further, we use these density functions to design feedback controllers capable of navigating in cluttered environments and high-dimensional configuration spaces. The proposed analytical construction of density functions overcomes the problem associated with navigation functions, which are known to exist but challenging to construct, and potential functions, which suffer from local minima. Application of the developed framework is demonstrated on simple integrator dynamics and fully actuated robotic systems.

cs.RO↗

arXiv2023

The Limits to Learning a Diffusion Model

This paper provides the first sample complexity lower bounds for the estimation of simple diffusion models, including the Bass model (used in modeling consumer adoption) and the SIR model (used in modeling epidemics). We show that one cannot hope to learn such models until quite late in the diffusion. Specifically, we show that the time required to collect a number of observations that exceeds our sample complexity lower bounds is large. For Bass models with low innovation rates, our results imply that one cannot hope to predict the eventual number of adopting customers until one is at least two-thirds of the way to the time at which the rate of new adopters is at its peak. In a similar vein, our results imply that in the case of an SIR model, one cannot hope to predict the eventual number of infections until one is approximately two-thirds of the way to the time at which the infection rate has peaked. This lower bound in estimation further translates into a lower bound in regret for decision-making in epidemic interventions. Our results formalize the challenge of accurate forecasting and highlight the importance of incorporating additional data sources. To this end, we analyze the benefit of a seroprevalence study in an epidemic, where we characterize the size of the study needed to improve SIR model estimation. Extensive empirical analyses on product adoption and epidemic data support our theoretical findings.

stat.ME↗

arXiv2023

Correcting for Interference in Experiments: A Case Study at Douyin

Interference is a ubiquitous problem in experiments conducted on two-sided content marketplaces, such as Douyin (China's analog of TikTok). In many cases, creators are the natural unit of experimentation, but creators interfere with each other through competition for viewers' limited time and attention. "Naive" estimators currently used in practice simply ignore the interference, but in doing so incur bias on the order of the treatment effect. We formalize the problem of inference in such experiments as one of policy evaluation. Off-policy estimators, while unbiased, are impractically high variance. We introduce a novel Monte-Carlo estimator, based on "Differences-in-Qs" (DQ) techniques, which achieves bias that is second-order in the treatment effect, while remaining sample-efficient to estimate. On the theoretical side, our contribution is to develop a generalized theory of Taylor expansions for policy evaluation, which extends DQ theory to all major MDP formulations. On the practical side, we implement our estimator on Douyin's experimentation platform, and in the process develop DQ into a truly "plug-and-play" estimator for interference in real-world settings: one which provides robust, low-bias, low-variance treatment effect estimates; admits computationally cheap, asymptotically exact uncertainty quantification; and reduces MSE by 99\% compared to the best existing alternatives in our applications.

stat.ME↗

arXiv2023

Off-Road Navigation of Legged Robots Using Linear Transfer Operators

This paper presents the implementation of off-road navigation on legged robots using convex optimization through linear transfer operators. Given a traversability measure that captures the off-road environment, we lift the navigation problem into the density space using the Perron-Frobenius (P-F) operator. This allows the problem formulation to be represented as a convex optimization. Due to the operator acting on an infinite-dimensional density space, we use data collected from the terrain to get a finite-dimension approximation of the convex optimization. Results of the optimal trajectory for off-road navigation are compared with a standard iterative planner, where we show how our convex optimization generates a more traversable path for the legged robot compared to the suboptimal iterative planner.

cs.RO↗

arXiv2022

Markovian Interference in Experiments

We consider experiments in dynamical systems where interventions on some experimental units impact other units through a limiting constraint (such as a limited inventory). Despite outsize practical importance, the best estimators for this `Markovian' interference problem are largely heuristic in nature, and their bias is not well understood. We formalize the problem of inference in such experiments as one of policy evaluation. Off-policy estimators, while unbiased, apparently incur a large penalty in variance relative to state-of-the-art heuristics. We introduce an on-policy estimator: the Differences-In-Q's (DQ) estimator. We show that the DQ estimator can in general have exponentially smaller variance than off-policy evaluation. At the same time, its bias is second order in the impact of the intervention. This yields a striking bias-variance tradeoff so that the DQ estimator effectively dominates state-of-the-art alternatives. From a theoretical perspective, we introduce three separate novel techniques that are of independent interest in the theory of Reinforcement Learning (RL). Our empirical evaluation includes a set of experiments on a city-scale ride-hailing simulator.

cs.LG↗

arXiv2022

Synthetically Controlled Bandits

This paper presents a new dynamic approach to experiment design in settings where, due to interference or other concerns, experimental units are coarse. `Region-split' experiments on online platforms are one example of such a setting. The cost, or regret, of experimentation is a natural concern here. Our new design, dubbed Synthetically Controlled Thompson Sampling (SCTS), minimizes the regret associated with experimentation at no practically meaningful loss to inferential ability. We provide theoretical guarantees characterizing the near-optimal regret of our approach, and the error rates achieved by the corresponding treatment effect estimator. Experiments on synthetic and real world data highlight the merits of our approach relative to both fixed and `switchback' designs common to such experimental settings.

stat.ML↗

arXiv2019

Computing Estimators of Dantzig Selector type via Column and Constraint Generation

We consider a class of linear-programming based estimators in reconstructing a sparse signal from linear measurements. Specific formulations of the reconstruction problem considered here include Dantzig selector, basis pursuit (for the case in which the measurements contain no errors), and the fused Dantzig selector (for the case in which the underlying signal is piecewise constant). In spite of being estimators central to sparse signal processing and machine learning, solving these linear programming problems for large scale instances remains a challenging task, thereby limiting their usage in practice. We show that classic constraint- and column-generation techniques from large scale linear programming, when used in conjunction with a commercial implementation of the simplex method, and initialized with the solution from a closely-related Lasso formulation, yields solutions with high efficiency in many settings.

stat.CO↗