arXiv subjects

Ufuk Topcu

Publications and source records attributed to Ufuk Topcu.

At least 253 records · Page 14Linked to original sources

arXiv2021

Robust Finite-State Controllers for Uncertain POMDPs

Uncertain partially observable Markov decision processes (uPOMDPs) allow the probabilistic transition and observation functions of standard POMDPs to belong to a so-called uncertainty set. Such uncertainty, referred to as epistemic uncertainty, captures uncountable sets of probability distributions caused by, for instance, a lack of data available. We develop an algorithm to compute finite-memory policies for uPOMDPs that robustly satisfy specifications against any admissible distribution. In general, computing such policies is theoretically and practically intractable. We provide an efficient solution to this problem in four steps. (1) We state the underlying problem as a nonconvex optimization problem with infinitely many constraints. (2) A dedicated dualization scheme yields a dual problem that is still nonconvex but has finitely many constraints. (3) We linearize this dual problem and (4) solve the resulting finite linear program to obtain locally optimal solutions to the original problem. The resulting problem formulation is exponentially smaller than those resulting from existing methods. We demonstrate the applicability of our algorithm using large instances of an aircraft collision-avoidance scenario and a novel spacecraft motion planning case study.

cs.AI↗

arXiv2021

A 3D Printing Hexacopter: Design and Demonstration

3D printing using robots has garnered significant interest in manufacturing and construction in recent years. A robot's versatility paired with the design freedom of 3D printing offers promising opportunities for how parts and structures are built in the future. However, 3D printed objects are still limited in size and location due to a lack of vertical mobility of ground robots. These limitations severely restrict the potential of the 3D printing process. To overcome these limitations, we develop a hexacopter testbed that can print via fused deposition modeling during flight. We discuss the design of this testbed and develop a simple control strategy for initial print tests. By successfully performing these initial print tests, we demonstrate the feasibility of this approach and lay the groundwork for printing 3D parts and structures with drones.

cs.RO↗

arXiv2021

Smooth Convex Optimization using Sub-Zeroth-Order Oracles

We consider the problem of minimizing a smooth, Lipschitz, convex function over a compact, convex set using sub-zeroth-order oracles: an oracle that outputs the sign of the directional derivative for a given point and a given direction, an oracle that compares the function values for a given pair of points, and an oracle that outputs a noisy function value for a given point. We show that the sample complexity of optimization using these oracles is polynomial in the relevant parameters. The optimization algorithm that we provide for the comparator oracle is the first algorithm with a known rate of convergence that is polynomial in the number of dimensions. We also give an algorithm for the noisy-value oracle that incurs a regret of $\tilde{\mathcal{O}}(n^{3.75} T^{0.75})$ (ignoring the other factors and logarithmic dependencies) where $n$ is the number of dimensions and $T$ is the number of queries.

math.OC↗

arXiv2021

Physical-Layer Security via Distributed Beamforming in the Presence of Adversaries with Unknown Locations

We study the problem of securely communicating a sequence of information bits with a client in the presence of multiple adversaries at unknown locations in the environment. We assume that the client and the adversaries are located in the far-field region, and all possible directions for each adversary can be expressed as a continuous interval of directions. In such a setting, we develop a periodic transmission strategy, i.e., a sequence of joint beamforming gain and artificial noise pairs, that prevents the adversaries from decreasing their uncertainty on the information sequence by eavesdropping on the transmission. We formulate a series of nonconvex semi-infinite optimization problems to synthesize the transmission strategy. We show that the semi-definite program (SDP) relaxations of these nonconvex problems are exact under an efficiently verifiable sufficient condition. We approximate the SDP relaxations, which are subject to infinitely many constraints, by randomly sampling a finite subset of the constraints and establish the probability with which optimal solutions to the obtained finite SDPs and the semi-infinite SDPs coincide. We demonstrate with numerical simulations that the proposed periodic strategy can ensure the security of communication in scenarios in which all stationary strategies fail to guarantee security.

eess.SP↗

arXiv2021

Reward Machines for Cooperative Multi-Agent Reinforcement Learning

In cooperative multi-agent reinforcement learning, a collection of agents learns to interact in a shared environment to achieve a common goal. We propose the use of reward machines (RM) -- Mealy machines used as structured representations of reward functions -- to encode the team's task. The proposed novel interpretation of RMs in the multi-agent setting explicitly encodes required teammate interdependencies, allowing the team-level task to be decomposed into sub-tasks for individual agents. We define such a notion of RM decomposition and present algorithmically verifiable conditions guaranteeing that distributed completion of the sub-tasks leads to team behavior accomplishing the original task. This framework for task decomposition provides a natural approach to decentralized learning: agents may learn to accomplish their sub-tasks while observing only their local state and abstracted representations of their teammates. We accordingly propose a decentralized q-learning algorithm. Furthermore, in the case of undiscounted rewards, we use local value functions to derive lower and upper bounds for the global value function corresponding to the team task. Experimental results in three discrete settings exemplify the effectiveness of the proposed RM decomposition approach, which converges to a successful team policy an order of magnitude faster than a centralized learner and significantly outperforms hierarchical and independent q-learning approaches.

cs.MA↗

arXiv2021

Learning and Planning for Time-Varying MDPs Using Maximum Likelihood Estimation

This paper proposes a formal approach to online learning and planning for agents operating in a priori unknown, time-varying environments. The proposed method computes the maximally likely model of the environment, given the observations about the environment made by an agent earlier in the system run and assuming knowledge of a bound on the maximal rate of change of system dynamics. Such an approach generalizes the estimation method commonly used in learning algorithms for unknown Markov decision processes with time-invariant transition probabilities, but is also able to quickly and correctly identify the system dynamics following a change. Based on the proposed method, we generalize the exploration bonuses used in learning for time-invariant Markov decision processes by introducing a notion of uncertainty in a learned time-varying model, and develop a control policy for time-varying Markov decision processes based on the exploitation and exploration trade-off. We demonstrate the proposed methods on four numerical examples: a patrolling task with a change in system dynamics, a two-state MDP with periodically changing outcomes of actions, a wind flow estimation task, and a multi-armed bandit problem with periodically changing probabilities of different rewards.

cs.LG↗

arXiv2021

Controller Synthesis for Multi-Agent Systems with Intermittent Communication and Metric Temporal Logic Specifications

This paper investigates the controller synthesis problem for a multi-agent system (MAS) with intermittent communication. We adopt a relay-explorer scheme, where a mobile relay agent with absolute position sensors switches among a set of explorers with relative position sensors to provide intermittent state information. We model the MAS as a switched system where the explorers' dynamics can be either fully-actuated or underactuated. The objective of the explorers is to reach approximate consensus to a predetermined goal region. To guarantee the stability of the switched system and the approximate consensus of the explorers, we derive maximum dwell-time conditions to constrain the length of time each explorer goes without state feedback (from the relay agent). Furthermore, the relay agent needs to satisfy practical constraints such as charging its battery and staying in specific regions of interest. Both the maximum dwell-time conditions and these practical constraints can be expressed by metric temporal logic (MTL) specifications. We iteratively compute the optimal control inputs for the relay agent to satisfy the MTL specifications, while guaranteeing stability and approximate consensus of the explorers. We implement the proposed method on a case study with the CoppeliaSim robot simulator.

cs.RO↗

arXiv2021

Safe Multi-Agent Reinforcement Learning via Shielding

Multi-agent reinforcement learning (MARL) has been increasingly used in a wide range of safety-critical applications, which require guaranteed safety (e.g., no unsafe states are ever visited) during the learning process.Unfortunately, current MARL methods do not have safety guarantees. Therefore, we present two shielding approaches for safe MARL. In centralized shielding, we synthesize a single shield to monitor all agents' joint actions and correct any unsafe action if necessary. In factored shielding, we synthesize multiple shields based on a factorization of the joint state space observed by all agents; the set of shields monitors agents concurrently and each shield is only responsible for a subset of agents at each step.Experimental results show that both approaches can guarantee the safety of agents during learning without compromising the quality of learned policies; moreover, factored shielding is more scalable in the number of agents than centralized shielding.

cs.LG↗

arXiv2020

Multiple Plans are Better than One: Diverse Stochastic Planning

In planning problems, it is often challenging to fully model the desired specifications. In particular, in human-robot interaction, such difficulty may arise due to human's preferences that are either private or complex to model. Consequently, the resulting objective function can only partially capture the specifications and optimizing that may lead to poor performance with respect to the true specifications. Motivated by this challenge, we formulate a problem, called diverse stochastic planning, that aims to generate a set of representative -- small and diverse -- behaviors that are near-optimal with respect to the known objective. In particular, the problem aims to compute a set of diverse and near-optimal policies for systems modeled by a Markov decision process. We cast the problem as a constrained nonlinear optimization for which we propose a solution relying on the Frank-Wolfe method. We then prove that the proposed solution converges to a stationary point and demonstrate its efficacy in several planning problems.

cs.RO↗

arXiv2020

Constrained, Global Optimization of Functions with Lipschitz Continuous Gradients

We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous gradients. The proposed algorithms balance the exploration of the a priori unknown feasible space with the pursuit of global optimality within in a pre-specified finite number of first-order oracle calls. The first algorithm accommodates an infeasible start, and provides either a near-optimal global solution or establishes infeasibility. However, the algorithm may produce infeasible iterates during the search. For a strongly-convex constraint function and a feasible initial solution guess, the second algorithm returns a near-optimal global solution without any constraint violation. In contrast to existing methods, both of the algorithms also compute global suboptimality bounds at every iteration. We also show that the algorithms can satisfy user-specified tolerances in the computed solution with near-optimal complexity in oracle calls for a large class of optimization problems. We propose tractable implementations of the algorithms by exploiting the structure afforded by the Lipschitz continuous gradient property.

math.OC↗

arXiv2020

Assured Autonomy: Path Toward Living With Autonomous Systems We Can Trust

The challenge of establishing assurance in autonomy is rapidly attracting increasing interest in the industry, government, and academia. Autonomy is a broad and expansive capability that enables systems to behave without direct control by a human operator. To that end, it is expected to be present in a wide variety of systems and applications. A vast range of industrial sectors, including (but by no means limited to) defense, mobility, health care, manufacturing, and civilian infrastructure, are embracing the opportunities in autonomy yet face the similar barriers toward establishing the necessary level of assurance sooner or later. Numerous government agencies are poised to tackle the challenges in assured autonomy. Given the already immense interest and investment in autonomy, a series of workshops on Assured Autonomy was convened to facilitate dialogs and increase awareness among the stakeholders in the academia, industry, and government. This series of three workshops aimed to help create a unified understanding of the goals for assured autonomy, the research trends and needs, and a strategy that will facilitate sustained progress in autonomy. The first workshop, held in October 2019, focused on current and anticipated challenges and problems in assuring autonomous systems within and across applications and sectors. The second workshop held in February 2020, focused on existing capabilities, current research, and research trends that could address the challenges and problems identified in workshop. The third event was dedicated to a discussion of a draft of the major findings from the previous two workshops and the recommendations.

cs.CY↗

arXiv2020

Minimum-Violation Planning for Autonomous Systems: Theoretical and Practical Considerations

This paper considers the problem of computing an optimal trajectory for an autonomous system that is subject to a set of potentially conflicting rules. First, we introduce the concept of prioritized safety specifications, where each rule is expressed as a temporal logic formula with its associated weight and priority. The optimality is defined based on the violation of such prioritized safety specifications. We then introduce a class of temporal logic formulas called $\textrm{si-FLTL}_{\mathsf{G_X}}$ and develop an efficient, incremental sampling-based approach to solve this minimum-violation planning problem with guarantees on asymptotic optimality. We illustrate the application of the proposed approach in autonomous vehicles, showing that $\textrm{si-FLTL}_{\mathsf{G_X}}$ formulas are sufficiently expressive to describe many traffic rules. Finally, we discuss practical considerations and present simulation results for a vehicle overtaking scenario.

cs.RO↗

arXiv2020

Active Task-Inference-Guided Deep Inverse Reinforcement Learning

We consider the problem of reward learning for temporally extended tasks. For reward learning, inverse reinforcement learning (IRL) is a widely used paradigm. Given a Markov decision process (MDP) and a set of demonstrations for a task, IRL learns a reward function that assigns a real-valued reward to each state of the MDP. However, for temporally extended tasks, the underlying reward function may not be expressible as a function of individual states of the MDP. Instead, the history of visited states may need to be considered to determine the reward at the current state. To address this issue, we propose an iterative algorithm to learn a reward function for temporally extended tasks. At each iteration, the algorithm alternates between two modules, a task inference module that infers the underlying task structure and a reward learning module that uses the inferred task structure to learn a reward function. The task inference module produces a series of queries, where each query is a sequence of subgoals. The demonstrator provides a binary response to each query by attempting to execute it in the environment and observing the environment's feedback. After the queries are answered, the task inference module returns an automaton encoding its current hypothesis of the task structure. The reward learning module augments the state space of the MDP with the states of the automaton. The module then proceeds to learn a reward function over the augmented state space using a novel deep maximum entropy IRL algorithm. This iterative process continues until it learns a reward function with satisfactory performance. The experiments show that the proposed algorithm significantly outperforms several IRL baselines on temporally extended tasks.

cs.RO↗

arXiv2020

BP-RRT: Barrier Pair Synthesis for Temporal Logic Motion Planning

For a nonlinear system (e.g. a robot) with its continuous state space trajectories constrained by a linear temporal logic specification, the synthesis of a low-level controller for mission execution often results in a non-convex optimization problem. We devise a new algorithm to solve this type of non-convex problems by formulating a rapidly-exploring random tree of barrier pairs, with each barrier pair composed of a quadratic barrier function and a full state feedback controller. The proposed method employs a rapid-exploring random tree to deal with the non-convex constraints and uses barrier pairs to fulfill the local convex constraints. As such, the method solves control problems fulfilling the required transitions of an automaton in order to satisfy given linear temporal logic constraints. At the same time it synthesizes locally optimal controllers in order to transition between the regions corresponding to the alphabet of the automaton. We demonstrate this new algorithm on a simulation of a two linkage manipulator robot.

cs.RO↗

arXiv2020

Control Strategies for COVID-19 Epidemic with Vaccination, Shield Immunity and Quarantine: A Metric Temporal Logic Approach

Ever since the outbreak of the COVID-19 epidemic, various public health control strategies have been proposed and tested against the coronavirus SARS-CoV-2. We study three specific COVID-19 epidemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control; the SEIR model with shield immunity control; and the susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC) model with quarantine control. We express the control requirement in metric temporal logic (MTL) formulas (a type of formal specification languages) which can specify the expected control outcomes such as "the deaths from the infection should never exceed one thousand per day within the next three months" or "the population immune from the disease should eventually exceed 200 thousand within the next 100 to 120 days". We then develop methods for synthesizing control strategies with MTL specifications. To the best of our knowledge, this is the first paper to systematically synthesize control strategies based on the COVID-19 epidemic models with formal specifications. We provide simulation results in three different case studies: vaccination control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; shield immunity control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; and quarantine control for the COVID-19 epidemic with model parameters estimated from data in Wuhan, China. The results show that the proposed synthesis approach can generate control inputs such that the time-varying numbers of individuals in each category (e.g., infectious, immune) satisfy the MTL specifications. The results also show that early intervention is essential in mitigating the spread of COVID-19, and more control effort is needed for more stringent MTL specifications.

eess.SY↗

arXiv2020

Near-Optimal Reactive Synthesis Incorporating Runtime Information

We consider the problem of optimal reactive synthesis - compute a strategy that satisfies a mission specification in a dynamic environment, and optimizes a performance metric. We incorporate task-critical information, that is only available at runtime, into the strategy synthesis in order to improve performance. Existing approaches to utilising such time-varying information require online re-synthesis, which is not computationally feasible in real-time applications. In this paper, we pre-synthesize a set of strategies corresponding to candidate instantiations (pre-specified representative information scenarios). We then propose a novel switching mechanism to dynamically switch between the strategies at runtime while guaranteeing all safety and liveness goals are met. We also characterize bounds on the performance suboptimality. We demonstrate our approach on two examples - robotic motion planning where the likelihood of the position of the robot's goal is updated in real-time, and an air traffic management problem for urban air mobility.

cs.RO↗

arXiv2020

Blending Controllers via Multi-Objective Bandits

Safety and performance are often two competing objectives in sequential decision-making problems. Existing performant controllers, such as controllers derived from reinforcement learning algorithms, often fall short of safety guarantees. On the contrary, controllers that guarantee safety, such as those derived from classical control theory, require restrictive assumptions and are often conservative in performance. Our goal is to blend a performant and a safe controller to generate a single controller that is safer than the performant and accumulates higher rewards than the safe controller. To this end, we propose a blending algorithm using the framework of contextual multi-armed multi-objective bandits. At each stage, the algorithm observes the environment's current context alongside an immediate reward and cost, which is the underlying safety measure. The algorithm then decides which controller to employ based on its observations. We demonstrate that the algorithm achieves sublinear Pareto regret, a performance measure that models coherence with an expert that always avoids picking the controller with both inferior safety and performance. We derive an upper bound on the loss in individual objectives, which imposes no additional computational complexity. We empirically demonstrate the algorithm's success in blending a safe and a performant controller in a safety-focused testbed, the Safety Gym environment. A statistical analysis of the blended controller's total reward and cost reflects two key takeaways: The blended controller shows a strict improvement in performance compared to the safe controller, and it is safer than the performant controller.

eess.SY↗

arXiv2020

On the Complexity of Sequential Incentive Design

In many scenarios, a principal dynamically interacts with an agent and offers a sequence of incentives to align the agent's behavior with a desired objective. This paper focuses on the problem of synthesizing an incentive sequence that, once offered, induces the desired agent behavior even when the agent's intrinsic motivation is unknown to the principal. We model the agent's behavior as a Markov decision process, express its intrinsic motivation as a reward function, which belongs to a finite set of possible reward functions, and consider the incentives as additional rewards offered to the agent. We first show that the behavior modification problem (BMP), i.e., the problem of synthesizing an incentive sequence that induces a desired agent behavior at minimum total cost to the principal, is PSPACE-hard. Moreover, we show that by imposing certain restrictions on the incentive sequences available to the principal, one can obtain two NP-complete variants of the BMP. We also provide a sufficient condition on the set of possible reward functions under which the BMP can be solved via linear programming. Finally, we propose two algorithms to compute globally and locally optimal solutions to the NP-complete variants of the BMP.

math.OC↗