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Risk sensitivity is a fundamental aspect of biological motor control that accounts for both the expectation and variability of movement cost in the face of uncertainty. However, most computational models of biological motor control rely on model-based risk-sensitive optimal control, which requires an accurate internal representation in the central neural system to predict the outcomes of motor commands. In reality, the dynamics of human-environment interaction is too complex to be accurately modeled, and noise further complicates system identification. To address this issue, this paper proposes a novel risk-sensitive computational mechanism for biological motor control based on reinforcement learning (RL) and adaptive dynamic programming (ADP). The proposed ADP-based mechanism suggests that humans can directly learn an approximation of the risk-sensitive optimal feedback controller from noisy sensory data without the need for system identification. Numerical validation of the proposed mechanism is conducted on the arm-reaching task under divergent force field. The preliminary computational results align with the experimental observations from the past literature of computational neuroscience. 

This paper presents a novel learning-based adaptive optimal controller design for linear time-delay systems described by delay differential equations (DDEs). A key strategy is to exploit the value iteration (VI) approach to solve the linear quadratic optimal control problem for time-delay systems. However, previous learning-based control methods are all exclusively devoted to discrete-time time-delay systems. In this article, we aim to fill in the gap by developing a learning-based VI approach to solve the infinite-dimensional algebraic Riccati equation (ARE) for continuous-time time-delay systems. One nice feature of the proposed VI approach is that an initial admissible controller is not required to start the algorithm. The efficacy of the proposed methodology is demonstrated by the example of autonomous driving. 

This paper presents a unified approach to the problem of learning-based optimal control of connected human-driven and autonomous vehicles in mixed-traffic environments including both the freeway and ring road settings. The stabilizability of a string of connected vehicles including multiple autonomous vehicles (AVs) and heterogeneous human-driven vehicles (HDVs) is studied by a model reduction technique and the Popov-Belevitch-Hautus (PBH) test. For this problem setup, a linear quadratic regulator (LQR) problem is formulated and a solution based on adaptive dynamic programming (ADP) techniques is proposed without a priori knowledge on model parameters. To start the learning process, an initial stabilizing control law is obtained using the small-gain theorem for the ring road case. It is shown that the obtained stabilizing control law can achieve general Lp string stability under appropriate conditions. Besides, to minimize the impact of external disturbance, a linear quadratic zero-sum game is introduced and solved by an iterative learning-based algorithm. Finally, the simulation results verify the theoretical analysis and the proposed methods achieve desirable performance for control of a mixed-vehicular network. 

This paper studies the learning-based optimal control for a class of infinite-dimensional linear time-delay systems. The aim is to fill the gap of adaptive dynamic programming (ADP) where adaptive optimal control of infinite-dimensional systems is not addressed. A key strategy is to combine the classical model-based linear quadratic (LQ) optimal control of time-delay systems with the state-of-art reinforcement learning (RL) technique. Both the model-based and data-driven policy iteration (PI) approaches are proposed to solve the corresponding algebraic Riccati equation (ARE) with guaranteed convergence. The proposed PI algorithm can be considered as a generalization of ADP to infinite-dimensional time-delay systems. The efficiency of the proposed algorithm is demonstrated by the practical application arising from autonomous driving in mixed traffic environments, where human drivers’ reaction delay is considered. 

This paper studies the adaptive optimal control problem for a class of linear time-delay systems described by delay differential equations (DDEs). A crucial strategy is to take advantage of recent developments in reinforcement learning (RL) and adaptive dynamic programming (ADP) and develop novel methods to learn adaptive optimal controllers from finite samples of input and state data. In this paper, the data-driven policy iteration (PI) is proposed to solve the infinite-dimensional algebraic Riccati equation (ARE) iteratively in the absence of exact model knowledge. Interestingly, the proposed recursive PI algorithm is new in the present context of continuous-time time-delay systems, even when the model knowledge is assumed known. The efficacy of the proposed learning-based control methods is validated by means of practical applications arising from metal cutting and autonomous driving. 

This article studies the adaptive optimal stationary control of continuous-time linear stochastic systems with both additive and multiplicative noises, using reinforcement learning techniques. Based on policy iteration, a novel off-policy reinforcement learning algorithm, named optimistic least-squares-based policy iteration, is proposed, which is able to find iteratively near-optimal policies of the adaptive optimal stationary control problem directly from input/state data without explicitly identifying any system matrices, starting from an initial admissible control policy. The solutions given by the proposed optimistic least-squares-based policy iteration are proved to converge to a small neighborhood of the optimal solution with probability one, under mild conditions. The application of the proposed algorithm to a triple inverted pendulum example validates its feasibility and effectiveness. 

Noises are ubiquitous in sensorimotor interactions and contaminate the information provided to the central nervous system (CNS) for motor learning. An interesting question is how the CNS manages motor learning with imprecise information. Integrating ideas from reinforcement learning and adaptive optimal control, this paper develops a novel computational mechanism to explain the robustness of human motor learning to the imprecise information, caused by control-dependent noise that exists inherently in the sensorimotor systems. Starting from an initial admissible control policy, in each learning trial the mechanism collects and uses the noisy sensory data (caused by the control-dependent noise) to form an imprecise evaluation of the performance of the current policy and then constructs an updated policy based on the imprecise evaluation. As the number of learning trials increases, the generated policies mathematically provably converge to a (potentially small) neighborhood of the optimal policy under mild conditions, despite the imprecise information in the learning process. The mechanism directly synthesizes the policies from the sensory data, without identifying an internal forward model. Our preliminary computational results on two classic arm reaching tasks are in line with experimental observations reported in the literature. The model-free control principle proposed in the paper sheds more lights into the inherent robustness of human sensorimotor systems to the imprecise information, especially control-dependent noise, in the CNS. 

This paper presents a data-driven algorithm to solve the problem of infinite-horizon linear quadratic regulation (LQR), for a class of discrete-time linear time-invariant systems subjected to state and control constraints. The problem is divided into a constrained finite-horizon LQR subproblem and an unconstrained infinite-horizon LQR subproblem, which can be solved directly from collected input/state data, separately. Under certain conditions, the combination of the solutions of the subproblems converges to the optimal solution of the original problem. The effectiveness of the proposed approach is validated by a numerical example. 

Recently, Quach, Wee and Wichs (FOCS 2018) proposed a new powerful cryptographic primitive called laconic function evaluation (LFE). Using an LFE scheme, Alice can compress a large circuit f into a small digest. Bob can encrypt some data x under this digest in a way that enables Alice to recover f(x) without learning anything else about Bob’s data. The laconic property requires that the size of the digest, the run-time of the encryption algorithm and the size of the ciphertext should be much smaller than the circuit-size of f. This new tool is motivated by an interesting application of “Bob-optimized” two-round secure two-party computation (2PC). In such a 2PC, Alice will get the final result thus the workload of Bob will be minimized. In this paper, we consider a “client-optimized” two-round secure multiparty computation, in which multiple clients provide inputs and enable a server to obtain final outputs while protecting privacy of each individual input. More importantly, we would also minimize the cost of each client. For this purpose, we propose multi-input laconic function evaluation (MI-LFE), and give a systematic study of it. It turns out that MI-LFE for general circuit is not easy. Specifically, we first show that the directly generalized version, i.e., the public-key MI-LFE implies virtual black-box obfuscation. Hence the public-key MI-LFE (for general circuits) is infeasible. This forces us to turn to secret key version of MI-LFE, in which encryption now needs to take a secret key. Next we show that secret-key MI-LFE also implies heavy cryptographic primitives including witness encryption for NP language and the indistinguishability obfuscation. On the positive side, we show that the secret-key MI-LFE can be constructed assuming indistinguishability obfuscation and learning with errors assumption. Our theoretical results suggest that we may have to explore relaxed versions of MI-LFE for meaningful new applications of “client-optimized” MPC and others.