Autonomous motion planning under unknown nonlinear dynamics presents significant challenges. An agent needs to continuously explore the system dynamics to acquire its properties, such as reachability, in order to guide system navigation adaptively. In this paper, we propose a hybrid planning-control framework designed to compute a feasible trajectory toward a target. Our approach involves partitioning the state space and approximating the system by a piecewise affine (PWA) system with constrained control inputs. By abstracting the PWA system into a directed weighted graph, we incrementally update the existence of its edges via affine system identification and reach control theory, introducing a predictive reachability condition by exploiting prior information of the unknown dynamics. Heuristic weights are assigned to edges based on whether their existence is certain or remains indeterminate. Consequently, we propose a framework that adaptively collects and analyzes data during mission execution, continually updates the predictive graph, and synthesizes a controller online based on the graph search outcomes. We demonstrate the efficacy of our approach through simulation scenarios involving a mobile robot operating in unknown terrains, with its unknown dynamics abstracted as a single integrator model.

Many real-world sequential repair problems can be effectively modeled using monotonic Markov Decision Processes (MDPs), where the system state stochastically decreases and can only be increased by performing a restorative action. This work addresses the problem of solving multi-component monotonic MDPs with both budget and capacity constraints. The budget constraint limits the total number of restorative actions and the capacity constraint limits the number of restorative actions that can be performed simultaneously. While prior methods dealt with budget constraints, including capacity constraints in prior methods leads to an exponential increase in computational complexity as the number of components in the MDP grows. We propose a two-step planning approach to address this challenge. First, we partition the components of the multi-component MDP into groups, where the number of groups is determined by the capacity constraint. We achieve this partitioning by solving a Linear Sum Assignment Problem (LSAP). Each group is then allocated a fraction of the total budget proportional to its size. This partitioning effectively decouples the large multi-component MDP into smaller subproblems, which are computationally feasible because the capacity constraint is simplified and the budget constraint can be addressed using existing methods. Subsequently, we use a meta-trained PPO agent to obtain an approximately optimal policy for each group. To validate our approach, we apply it to the problem of scheduling repairs for a large group of industrial robots, constrained by a limited number of repair technicians and a total repair budget. Our results demonstrate that the proposed method outperforms baseline approaches in terms of maximizing the average uptime of the robot swarm, particularly for large swarm sizes.

This paper examines the challenges associated with achieving life-long superalignment in AI systems, particularly large language models (LLMs). Superalignment is a theoretical framework that aspires to ensure that superintelligent AI systems act in accordance with human values and goals. Despite its promising vision, we argue that achieving superalignment requires substantial changes in the current LLM architectures due to their inherent limitations in comprehending and adapting to the dynamic nature of these human ethics and evolving global scenarios. We dissect the challenges of encoding an ever-changing spectrum of human values into LLMs, highlighting the discrepancies between static AI models and the dynamic nature of human societies. To illustrate these challenges, we analyze two distinct examples: one demonstrates a qualitative shift in human values, while the other presents a quantifiable change. Through these examples, we illustrate how LLMs, constrained by their training data, fail to align with contemporary human values and scenarios. The paper concludes by exploring potential strategies to address and possibly mitigate these alignment discrepancies, suggesting a path forward in the pursuit of more adaptable and responsive AI systems.

Optimal decision-making for trajectory tracking in partially observable, stochastic environments where the number of active localization updates -- the process by which the agent obtains its true state information from the sensors -- are limited, presents a significant challenge. Traditional methods often struggle to balance resource conservation, accurate state estimation and precise tracking, resulting in suboptimal performance. This problem is particularly pronounced in environments with large action spaces, where the need for frequent, accurate state data is paramount, yet the capacity for active localization updates is restricted by external limitations. This paper introduces ComTraQ-MPC, a novel framework that combines Deep Q-Networks (DQN) and Model Predictive Control (MPC) to optimize trajectory tracking with constrained active localization updates. The meta-trained DQN ensures adaptive active localization scheduling, while the MPC leverages available state information to improve tracking. The central contribution of this work is their reciprocal interaction: DQN's update decisions inform MPC's control strategy, and MPC's outcomes refine DQN's learning, creating a cohesive, adaptive system. Empirical evaluations in simulated and real-world settings demonstrate that ComTraQ-MPC significantly enhances operational efficiency and accuracy, providing a generalizable and approximately optimal solution for trajectory tracking in complex partially observable environments.

Partially Observable Markov Decision Processes (POMDPs) provide an efficient way to model real-world sequential decision making processes. Motivated by the problem of maintenance and inspection of a group of infrastructure components with independent dynamics, this paper presents an algorithm to find the optimal policy for a multi-component budget-constrained POMDP. We first introduce a budgeted-POMDP model (b-POMDP) which enables us to find the optimal policy for a POMDP while adhering to budget constraints. Next, we prove that the value function or maximal collected reward for a b-POMDP is a concave function of the budget for the finite horizon case. Our second contribution is an algorithm to calculate the optimal policy for a multi-component budget-constrained POMDP by finding the optimal budget split among the individual component POMDPs. The optimal budget split is posed as a welfare maximization problem and the solution is computed by exploiting the concave nature of the value function. We illustrate the effectiveness of the proposed algorithm by proposing a maintenance and inspection policy for a group of real-world infrastructure components with different deterioration dynamics, inspection and maintenance costs. We show that the proposed algorithm vastly outperforms the policy currently used in practice.