The optimality of allocating assets has been widely discussed with the theoretical analysis of risk measures. Pessimism is one of the most attractive approaches beyond the conventional optimal portfolio model, and the $\alpha$-risk plays a crucial role in deriving a broad class of pessimistic optimal portfolios. However, estimating an optimal portfolio assessed by a pessimistic risk is still challenging due to the absence of an available estimation model and a computational algorithm. In this study, we propose a version of integrated $\alpha$-risk called the uniform pessimistic risk and the computational algorithm to obtain an optimal portfolio based on the risk. Further, we investigate the theoretical properties of the proposed risk in view of three different approaches: multiple quantile regression, the proper scoring rule, and distributionally robust optimization. Also, the uniform pessimistic risk is applied to estimate the pessimistic optimal portfolio models for the Korean stock market and compare the result of the real data analysis. It is empirically confirmed that the proposed pessimistic portfolio presents a more robust performance than others when the stock market is unstable.
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We combine Tyler's robust estimator of the dispersion matrix with nonlinear shrinkage. This approach delivers a simple and fast estimator of the dispersion matrix in elliptical models that is robust against both heavy tails and high dimensions. We prove convergence of the iterative part of our algorithm and demonstrate the favorable performance of the estimator in a wide range of simulation scenarios. Finally, an empirical application demonstrates its state-of-the-art performance on real data.
This work presents the mechanical design and control of a novel small-size and lightweight Micro Aerial Vehicle (MAV) for aerial manipulation. To our knowledge, with a total take-off mass of only 2.0 kg, the proposed system is the most lightweight Aerial Manipulator (AM) that has 8-DOF independently controllable: 5 for the aerial platform and 3 for the articulated arm. We designed the robot to be fully-actuated in the body forward direction. This allows independent pitching and instantaneous force generation, improving the platform's performance during physical interaction. The robotic arm is an origami delta manipulator driven by three servomotors, enabling active motion compensation at the end-effector. Its composite multimaterial links help reduce the weight, while their flexibility allow for compliant aerial interaction with the environment. In particular, the arm's stiffness can be changed according to its configuration. We provide an in depth discussion of the system design and characterize the stiffness of the delta arm. A control architecture to deal with the platform's overactuation while exploiting the delta arm is presented. Its capabilities are experimentally illustrated both in free flight and physical interaction, highlighting advantages and disadvantages of the origami's folding mechanism.
Today's graphics processing unit (GPU) applications produce vast volumes of data, which are challenging to store and transfer efficiently. Thus, data compression is becoming a critical technique to mitigate the storage burden and communication cost. LZSS is the core algorithm in many widely used compressors, such as Deflate. However, existing GPU-based LZSS compressors suffer from low throughput due to the sequential nature of the LZSS algorithm. Moreover, many GPU applications produce multi-byte data (e.g., int16/int32 index, floating-point numbers), while the current LZSS compression only takes single-byte data as input. To this end, in this work, we propose GPULZ, a highly efficient LZSS compression on modern GPUs for multi-byte data. The contribution of our work is fourfold: First, we perform an in-depth analysis of existing LZ compressors for GPUs and investigate their main issues. Then, we propose two main algorithm-level optimizations. Specifically, we (1) change prefix sum from one pass to two passes and fuse multiple kernels to reduce data movement between shared memory and global memory, and (2) optimize existing pattern-matching approach for multi-byte symbols to reduce computation complexity and explore longer repeated patterns. Third, we perform architectural performance optimizations, such as maximizing shared memory utilization by adapting data partitions to different GPU architectures. Finally, we evaluate GPULZ on six datasets of various types with NVIDIA A100 and A4000 GPUs. Results show that GPULZ achieves up to 272.1X speedup on A4000 and up to 1.4X higher compression ratio compared to state-of-the-art solutions.
Neural networks are the state-of-the-art for many approximation tasks in high-dimensional spaces, as supported by an abundance of experimental evidence. However, we still need a solid theoretical understanding of what they can approximate and, more importantly, at what cost and accuracy. One network architecture of practical use, especially for approximation tasks involving images, is convolutional (residual) networks. However, due to the locality of the linear operators involved in these networks, their analysis is more complicated than for generic fully connected neural networks. This paper focuses on sequence approximation tasks, where a matrix or a higher-order tensor represents each observation. We show that when approximating sequences arising from space-time discretisations of PDEs we may use relatively small networks. We constructively derive these results by exploiting connections between discrete convolution and finite difference operators. Throughout, we design our network architecture to, while having guarantees, be similar to those typically adopted in practice for sequence approximation tasks. Our theoretical results are supported by numerical experiments which simulate linear advection, the heat equation, and the Fisher equation. The implementation used is available at the repository associated to the paper.
Necessary and sufficient conditions of uniform consistency are explored. Nonparametric sets of alternatives are bounded convex sets in $\mathbb{L}_p$ with "small" balls deleted. The "small" balls have the center at the point of hypothesis and radii of balls tend to zero as sample size increases. For problem of hypothesis testing on a density, we show that, for the sets of alternatives, there are uniformly consistent tests for some sequence of radii of the balls, if and only if, convex set is compact. The results are established for problem of hypothesis testing on a density, for signal detection in Gaussian white noise, for linear ill-posed problems with random Gaussian noise and so on.
Federated learning (FL) has become a popular tool for solving traditional Reinforcement Learning (RL) tasks. The multi-agent structure addresses the major concern of data-hungry in traditional RL, while the federated mechanism protects the data privacy of individual agents. However, the federated mechanism also exposes the system to poisoning by malicious agents that can mislead the trained policy. Despite the advantage brought by FL, the vulnerability of Federated Reinforcement Learning (FRL) has not been well-studied before. In this work, we propose the first general framework to characterize FRL poisoning as an optimization problem constrained by a limited budget and design a poisoning protocol that can be applied to policy-based FRL and extended to FRL with actor-critic as a local RL algorithm by training a pair of private and public critics. We also discuss a conventional defense strategy inherited from FL to mitigate this risk. We verify our poisoning effectiveness by conducting extensive experiments targeting mainstream RL algorithms and over various RL OpenAI Gym environments covering a wide range of difficulty levels. Our results show that our proposed defense protocol is successful in most cases but is not robust under complicated environments. Our work provides new insights into the vulnerability of FL in RL training and poses additional challenges for designing robust FRL algorithms.
We introduce and analyze a partially augmented fully-mixed formulation and a mixed finite element method for the coupled problem arising in the interaction between a free fluid and a poroelastic medium. The flows in the free fluid and poroelastic regions are governed by the Navier-Stokes and Biot equations, respectively, and the transmission conditions are given by mass conservation, balance of fluid force, conservation of momentum, and the Beavers-Joseph-Saffman condition. We apply dual-mixed formulations in both domains, where the symmetry of the Navier-Stokes and poroelastic stress tensors is imposed in an ultra-weak and weak sense. In turn, since the transmission conditions are essential in the fully mixed formulation, they are imposed weakly by introducing the traces of the structure velocity and the poroelastic medium pressure on the interface as the associated Lagrange multipliers. Furthermore, since the fluid convective term requires the velocity to live in a smaller space than usual, we augment the variational formulation with suitable Galerkin type terms. Existence and uniqueness of a solution are established for the continuous weak formulation, as well as a semidiscrete continuous-in-time formulation with non-matching grids, together with the corresponding stability bounds and error analysis with rates of convergence. Several numerical experiments are presented to verify the theoretical results and illustrate the performance of the method for applications to arterial flow and flow through a filter.
We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data while maintaining type I error control. We build upon the principle of (nonparametric) testing by betting, where a gambler places bets on future observations and their wealth measures evidence against the null hypothesis. While recently developed kernel-based betting strategies often work well on simple distributions, selecting a suitable kernel for high-dimensional or structured data, such as text and images, is often nontrivial. To address this drawback, we design prediction-based betting strategies that rely on the following fact: if a sequentially updated predictor starts to consistently determine (a) which distribution an instance is drawn from, or (b) whether an instance is drawn from the joint distribution or the product of the marginal distributions (the latter produced by external randomization), it provides evidence against the two-sample or independence nulls respectively. We empirically demonstrate the superiority of our tests over kernel-based approaches under structured settings. Our tests can be applied beyond the case of independent and identically distributed data, remaining valid and powerful even when the data distribution drifts over time.
Quantum algorithms for factorization, search, and simulation obtain computational advantage by performing control flow such as branching and iteration based on the value of quantum data in superposition. Complicating realization of these algorithms is the fact that in predominant quantum machine models, all control flow as embodied by the program counter is classical, and cannot exist in superposition. In this work, we identify that an alternative model to enable a program counter in superposition faces an obstacle -- no such machine can correctly support control flow constructs with non-injective semantics, including the conventional conditional jump. In fact, prior attempts to support this instruction cause programs to inappropriately collapse the superposition of data, meaning that quantum advantage is lost. We present a quantum machine model that supports both quantum effects on data and data-dependent control flow, using variants of conditional jump with injective semantics. We identify the necessary condition for programs for such a machine to preserve superposition of data, and show that expressible programs coincide with the unitary quantum circuits.
Ensuring Reliable Robot Task Performance through Probabilistic Rare-Event Verification and Synthesis
Providing guarantees on the safe operation of robots against edge cases is challenging as testing methods such as traditional Monte-Carlo require too many samples to provide reasonable statistics. Built upon recent advancements in rare-event sampling, we present a model-based method to verify if a robotic system satisfies a Signal Temporal Logic (STL) specification in the face of environment variations and sensor/actuator noises. Our method is efficient and applicable to both linear and nonlinear and even black-box systems with arbitrary, but known, uncertainty distributions. For linear systems with Gaussian uncertainties, we exploit a feature to find optimal parameters that minimize the probability of failure. We demonstrate illustrative examples on applying our approach to real-world autonomous robotic systems.
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