Dosing models often use differential equations to model biological dynamics.

Multi-task reinforcement learning endeavors to efficiently leverage shared information across various tasks, facilitating the simultaneous learning of multiple tasks. Existing approaches primarily focus on parameter sharing with carefully designed network structures or tailored optimization procedures. However, they overlook a direct and complementary way to exploit cross-task similarities: the control policies of tasks already proficient in some skills can provide explicit guidance for unmastered tasks to accelerate skills acquisition. To this end, we present a novel framework called Cross-Task Policy Guidance (CTPG), which trains a guide policy for each task to select the behavior policy interacting with the environment from all tasks' control policies, generating better training trajectories. In addition, we propose two gating mechanisms to improve the learning efficiency of CTPG: one gate filters out control policies that are not beneficial for guidance, while the other gate blocks tasks that do not necessitate guidance. CTPG is a general framework adaptable to existing parameter sharing approaches. Empirical evaluations demonstrate that incorporating CTPG with these approaches significantly enhances performance in manipulation and locomotion benchmarks.

Biological and artificial agents need to deal with constant changes in the real world. We study this problem in four classical continuous control environments, augmented with morphological perturbations. Learning to locomote when the length and the thickness of different body parts vary is challenging, as the control policy is required to adapt to the morphology to successfully balance and advance the agent. We show that a control policy based on the proprioceptive state performs poorly with highly variable body configurations, while an (oracle) agent with access to a learned encoding of the perturbation performs significantly better. We introduce DMAP, a biologically-inspired, attention-based policy network architecture. DMAP combines independent proprioceptive processing, a distributed policy with individual controllers for each joint, and an attention mechanism, to dynamically gate sensory information from different body parts to different controllers. Despite not having access to the (hidden) morphology information, DMAP can be trained end-to-end in all the considered environments, overall matching or surpassing the performance of an oracle agent. Thus DMAP, implementing principles from biological motor control, provides a strong inductive bias for learning challenging sensorimotor tasks.

Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations, subject to additive noise, with the goal of minimizing a quadratic cost function for the state and control variables. In this work, we consider a generalization of the discrete-time, finite-horizon LQG problem, where the noise distributions are unknown and belong to Wasserstein ambiguity sets centered at nominal (Gaussian) distributions. The objective is to minimize a worst-case cost across all distributions in the ambiguity set, including non-Gaussian distributions. Despite the added complexity, we prove that a control policy that is linear in the observations is optimal for this problem, as in the classic LQG problem. We propose a numerical solution method that efficiently characterizes this optimal control policy. Our method uses the Frank-Wolfe algorithm to identify the least-favorable distributions within the Wasserstein ambiguity sets and computes the controller's optimal policy using Kalman filter estimation under these distributions.

While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy. However, finding Lyapunov functions for general nonlinear systems is a challenging task. To address this challenge, several methods have been proposed that represent Lyapunov functions using neural networks. However, such approaches either focus on continuous-time systems, or highly restricted classes of nonlinear dynamics.

Data-driven methods have become paramount in modern systems and control problems characterized by growing levels of complexity . In safety-critical environments, deploying these methods requires rigorous guarantees, a need that has motivated much recent work at the interface of statistical learning and control. However, many existing approaches achieve this goal at the cost of sacrificing valuable data for testing and calibration, or by constraining the choice of learning algorithm, thus leading to suboptimal performances. In this paper, we describe Pick-to-Learn (P2L) for Systems and Control, a framework that allows any data-driven control method to be equipped with state-of-the-art safety and performance guarantees. P2L enables the use of all available data to jointly synthesize and certify the design, eliminating the need to set aside data for calibration or validation purposes. In presenting a comprehensive version of P2L for systems and control, this paper demonstrates its effectiveness across a range of core problems, including optimal control, reachability analysis, safe synthesis, and robust control. In many of these applications, P2L delivers designs and certificates that outperform commonly employed methods, and shows strong potential for broad applicability in diverse practical settings.

Data-driven motion priors that can guide agents toward producing naturalistic behaviors play a pivotal role in creating life-like virtual characters. Adversarial imitation learning has been a highly effective method for learning motion priors from reference motion data. However, adversarial priors, with few exceptions, need to be retrained for each new controller, thereby limiting their reusability and necessitating the retention of the reference motion data when training on downstream tasks. In this work, we present Score-Matching Motion Priors (SMP), which leverages pre-trained motion diffusion models and score distillation sampling (SDS) to create reusable task-agnostic motion priors. SMPs can be pre-trained on a motion dataset, independent of any control policy or task. Once trained, SMPs can be kept frozen and reused as general-purpose reward functions to train policies to produce naturalistic behaviors for downstream tasks. We show that a general motion prior trained on large-scale datasets can be repurposed into a variety of style-specific priors. Furthermore SMP can compose different styles to synthesize new styles not present in the original dataset. Our method produces high-quality motion comparable to state-of-the-art adversarial imitation learning methods through reusable and modular motion priors. We demonstrate the effectiveness of SMP across a diverse suite of control tasks with physically simulated humanoid characters. Video demo available at https://youtu.be/ravlZJteS20

Biotechnology can benefit from dynamic control to improve production efficiency. In this context, optogenetics enables modulation of gene expression using light as an external input, allowing fine-tuning of protein levels to unlock dynamic metabolic control and regulation of cell growth. Optogenetic systems can be actuated by light intensity. However, relying solely on intensity-driven control (i.e., signal amplitude) may fail to properly tune optogenetic bioprocesses when the dose-response relationship (i.e., light intensity versus gene-expression strength) is steep. In these cases, tunability is effectively constrained to either fully active or fully repressed gene expression, with little intermediate regulation. Pulse-width modulation, a concept widely used in electronics, can alleviate this issue by alternating between fully ON and OFF light intensity within forcing periods, thereby smoothing the average response and enhancing process controllability. Naturally, optimizing pulse-width-modulated optogenetics entails a switching-time optimal control problem with a binary input over many forcing periods. While this can be formulated as a mixed-integer program on a refined time grid, the number of decision variables can grow rapidly with increasing time-grid resolution and number of forcing periods, compromising tractability. Here, we propose an alternative solution based on reinforcement learning. We parametrize control actions via the duty cycle, a continuous variable that encodes the ON-to-OFF switching time within each forcing period, thereby respecting the intrinsic binary nature of the light intensity.

We introduce a new formulation of the Hidden Parameter Markov Decision Process (HiP-MDP), a framework for modeling families of related tasks using low-dimensional latent embeddings.