The present article explores the application of randomized control techniques in empirical asset pricing and performance evaluation. It introduces geometric random walks, a class of Markov chain Monte Carlo methods, to construct flexible control groups in the form of random portfolios adhering to investor constraints. The sampling-based methods enable an exploration of the relationship between academically studied factor premia and performance in a practical setting. In an empirical application, the study assesses the potential to capture premias associated with size, value, quality, and momentum within a strongly constrained setup, exemplified by the investor guidelines of the MSCI Diversified Multifactor index. Additionally, the article highlights issues with the more traditional use case of random portfolios for drawing inferences in performance evaluation, showcasing challenges related to the intricacies of high-dimensional geometry.
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We propose a novel gradient-based online optimization framework for solving stochastic programming problems that frequently arise in the context of cyber-physical and robotic systems. Our problem formulation accommodates constraints that model the evolution of a cyber-physical system, which has, in general, a continuous state and action space, is nonlinear, and where the state is only partially observed. We also incorporate an approximate model of the dynamics as prior knowledge into the learning process and show that even rough estimates of the dynamics can significantly improve the convergence of our algorithms. Our online optimization framework encompasses both gradient descent and quasi-Newton methods, and we provide a unified convergence analysis of our algorithms in a non-convex setting. We also characterize the impact of modeling errors in the system dynamics on the convergence rate of the algorithms. Finally, we evaluate our algorithms in simulations of a flexible beam, a four-legged walking robot, and in real-world experiments with a ping-pong playing robot.
This paper introduces a new resource allocation framework for integrated sensing and communication (ISAC) systems, which are expected to be fundamental aspects of sixth-generation networks. In particular, we develop an augmented Lagrangian manifold optimization (ALMO) framework designed to maximize communication sum rate while satisfying sensing beampattern gain targets and base station (BS) transmit power limits. ALMO applies the principles of Riemannian manifold optimization (MO) to navigate the complex, non-convex landscape of the resource allocation problem. It efficiently leverages the augmented Lagrangian method to ensure adherence to constraints. We present comprehensive numerical results to validate our framework, which illustrates the ALMO method's superior capability to enhance the dual functionalities of communication and sensing in ISAC systems. For instance, with 12 antennas and 30 dBm BS transmit power, our proposed ALMO algorithm delivers a 10.1% sum rate gain over a benchmark optimization-based algorithm. This work demonstrates significant improvements in system performance and contributes a new algorithmic perspective to ISAC resource management.
This paper proposes a simple generative model to detect change points in time series of graphs. The proposed framework consists of learnable prior distributions for low-dimensional graph representations and of a decoder that can generate dynamic graphs from the latent representations. The informative prior distributions in the latent spaces are learned from observed data as empirical Bayes, and the expressive power of a generative model is exploited to assist change point detection. Specifically, the model parameters are learned via maximum approximate likelihood, with a Group Fused Lasso regularization. The optimization problem is then solved via Alternating Direction Method of Multipliers (ADMM), and Langevin Dynamics are recruited for posterior inference. Experiments in simulated and real data demonstrate the ability of the generative model in supporting change point detection with good performance.
This article presents novel methods for synthesizing distributionally robust stabilizing neural controllers and certificates for control systems under model uncertainty. A key challenge in designing controllers with stability guarantees for uncertain systems is the accurate determination of and adaptation to shifts in model parametric uncertainty during online deployment. We tackle this with a novel distributionally robust formulation of the Lyapunov derivative chance constraint ensuring a monotonic decrease of the Lyapunov certificate. To avoid the computational complexity involved in dealing with the space of probability measures, we identify a sufficient condition in the form of deterministic convex constraints that ensures the Lyapunov derivative constraint is satisfied. We integrate this condition into a loss function for training a neural network-based controller and show that, for the resulting closed-loop system, the global asymptotic stability of its equilibrium can be certified with high confidence, even with Out-of-Distribution (OoD) model uncertainties. To demonstrate the efficacy and efficiency of the proposed methodology, we compare it with an uncertainty-agnostic baseline approach and several reinforcement learning approaches in two control problems in simulation.
We introduce a novel doubly-robust (DR) off-policy evaluation (OPE) estimator for Markov decision processes, DRUnknown, designed for situations where both the logging policy and the value function are unknown. The proposed estimator initially estimates the logging policy and then estimates the value function model by minimizing the asymptotic variance of the estimator while considering the estimating effect of the logging policy. When the logging policy model is correctly specified, DRUnknown achieves the smallest asymptotic variance within the class containing existing OPE estimators. When the value function model is also correctly specified, DRUnknown is optimal as its asymptotic variance reaches the semiparametric lower bound. We present experimental results conducted in contextual bandits and reinforcement learning to compare the performance of DRUnknown with that of existing methods.
The rapid advance of deep reinforcement learning techniques enables the oversight of safety-critical systems through the utilization of Deep Neural Networks (DNNs). This underscores the pressing need to promptly establish certified safety guarantees for such DNN-controlled systems. Most of the existing verification approaches rely on qualitative approaches, predominantly employing reachability analysis. However, qualitative verification proves inadequate for DNN-controlled systems as their behaviors exhibit stochastic tendencies when operating in open and adversarial environments. In this paper, we propose a novel framework for unifying both qualitative and quantitative safety verification problems of DNN-controlled systems. This is achieved by formulating the verification tasks as the synthesis of valid neural barrier certificates (NBCs). Initially, the framework seeks to establish almost-sure safety guarantees through qualitative verification. In cases where qualitative verification fails, our quantitative verification method is invoked, yielding precise lower and upper bounds on probabilistic safety across both infinite and finite time horizons. To facilitate the synthesis of NBCs, we introduce their $k$-inductive variants. We also devise a simulation-guided approach for training NBCs, aiming to achieve tightness in computing precise certified lower and upper bounds. We prototype our approach into a tool called $\textsf{UniQQ}$ and showcase its efficacy on four classic DNN-controlled systems.
We study evaluating a policy under best- and worst-case perturbations to a Markov decision process (MDP), given transition observations from the original MDP, whether under the same or different policy. This is an important problem when there is the possibility of a shift between historical and future environments, due to e.g. unmeasured confounding, distributional shift, or an adversarial environment. We propose a perturbation model that can modify transition kernel densities up to a given multiplicative factor or its reciprocal, which extends the classic marginal sensitivity model (MSM) for single time step decision making to infinite-horizon RL. We characterize the sharp bounds on policy value under this model, that is, the tightest possible bounds given by the transition observations from the original MDP, and we study the estimation of these bounds from such transition observations. We develop an estimator with several appealing guarantees: it is semiparametrically efficient, and remains so even when certain necessary nuisance functions such as worst-case Q-functions are estimated at slow nonparametric rates. It is also asymptotically normal, enabling easy statistical inference using Wald confidence intervals. In addition, when certain nuisances are estimated inconsistently we still estimate a valid, albeit possibly not sharp bounds on the policy value. We validate these properties in numeric simulations. The combination of accounting for environment shifts from train to test (robustness), being insensitive to nuisance-function estimation (orthogonality), and accounting for having only finite samples to learn from (inference) together leads to credible and reliable policy evaluation.
This article presents an analysis of current state-of-the-art sensors and how these sensors work with several mapping algorithms for UAV (Unmanned Aerial Vehicle) applications, focusing on low-altitude and high-speed scenarios. A new experimental construct is created using highly realistic environments made possible by integrating the AirSim simulator with Google 3D maps models using the Cesium Tiles plugin. Experiments are conducted in this high-realism simulated environment to evaluate the performance of three distinct mapping algorithms: (1) Direct Sparse Odometry (DSO), (2) Stereo DSO (SDSO), and (3) DSO Lite (DSOL). Experimental results evaluate algorithms based on their measured geometric accuracy and computational speed. The results provide valuable insights into the strengths and limitations of each algorithm. Findings quantify compromises in UAV algorithm selection, allowing researchers to find the mapping solution best suited to their application, which often requires a compromise between computational performance and the density and accuracy of geometric map estimates. Results indicate that for UAVs with restrictive computing resources, DSOL is the best option. For systems with payload capacity and modest compute resources, SDSO is the best option. If only one camera is available, DSO is the option to choose for applications that require dense mapping results.
This paper presents a formal verification guided approach for a principled design and implementation of robust and resilient learning-enabled systems. We focus on learning-enabled state estimation systems (LE-SESs), which have been widely used in robotics applications to determine the current state (e.g., location, speed, direction, etc.) of a complex system. The LE-SESs are networked systems, composed of a set of connected components including: Bayes filters for state estimation, and neural networks for processing sensory input. We study LE-SESs from the perspective of formal verification, which determines the satisfiabilty of a system model against the specified properties. Over LE-SESs, we investigate two key properties -- robustness and resilience -- and provide their formal definitions. To enable formal verification, we reduce the LE-SESs to a novel class of labelled transition systems, named {PO}^2-LTS in the paper, and formally express the properties as constrained optimisation objectives. We prove that the verification problems are NP-complete. Based on {PO}^2-LTS and the optimisation objectives, practical verification algorithms are developed to check the satisfiability of the properties on the LE-SESs. As a major case study, we interrogate a real-world dynamic tracking system which uses a single Kalman Filter (KF) -- a special case of Bayes filter -- to localise and track a ground vehicle. Its perception system, based on convolutional neural networks, processes a high-resolution Wide Area Motion Imagery (WAMI) data stream. Experimental results show that our algorithms can not only verify the properties of the WAMI tracking system but also provide representative examples, the latter of which inspired us to take an enhanced LE-SESs design where runtime monitors or joint-KFs are required. Experimental results confirm the improvement in the robustness of the enhanced design.
Molecular design and synthesis planning are two critical steps in the process of molecular discovery that we propose to formulate as a single shared task of conditional synthetic pathway generation. We report an amortized approach to generate synthetic pathways as a Markov decision process conditioned on a target molecular embedding. This approach allows us to conduct synthesis planning in a bottom-up manner and design synthesizable molecules by decoding from optimized conditional codes, demonstrating the potential to solve both problems of design and synthesis simultaneously. The approach leverages neural networks to probabilistically model the synthetic trees, one reaction step at a time, according to reactivity rules encoded in a discrete action space of reaction templates. We train these networks on hundreds of thousands of artificial pathways generated from a pool of purchasable compounds and a list of expert-curated templates. We validate our method with (a) the recovery of molecules using conditional generation, (b) the identification of synthesizable structural analogs, and (c) the optimization of molecular structures given oracle functions relevant to drug discovery.
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