arXiv subjects

Ufuk Topcu

Publications and source records attributed to Ufuk Topcu.

At least 217 records · Page 12Linked to original sources

arXiv2021

Learning to Reach, Swim, Walk and Fly in One Trial: Data-Driven Control with Scarce Data and Side Information

We develop a learning-based control algorithm for unknown dynamical systems under very severe data limitations. Specifically, the algorithm has access to streaming and noisy data only from a single and ongoing trial. It accomplishes such performance by effectively leveraging various forms of side information on the dynamics to reduce the sample complexity. Such side information typically comes from elementary laws of physics and qualitative properties of the system. More precisely, the algorithm approximately solves an optimal control problem encoding the system's desired behavior. To this end, it constructs and iteratively refines a data-driven differential inclusion that contains the unknown vector field of the dynamics. The differential inclusion, used in an interval Taylor-based method, enables to over-approximate the set of states the system may reach. Theoretically, we establish a bound on the suboptimality of the approximate solution with respect to the optimal control with known dynamics. We show that the longer the trial or the more side information is available, the tighter the bound. Empirically, experiments in a high-fidelity F-16 aircraft simulator and MuJoCo's environments illustrate that, despite the scarcity of data, the algorithm can provide performance comparable to reinforcement learning algorithms trained over millions of environment interactions. Besides, we show that the algorithm outperforms existing techniques combining system identification and model predictive control.

eess.SY↗

arXiv2021

On the Detection of Markov Decision Processes

We study the detection problem for a finite set of Markov decision processes (MDPs) where the MDPs have the same state and action spaces but possibly different probabilistic transition functions. Any one of these MDPs could be the model for some underlying controlled stochastic process, but it is unknown a priori which MDP is the ground truth. We investigate whether it is possible to asymptotically detect the ground truth MDP model perfectly based on a single observed history (state-action sequence). Since the generation of histories depends on the policy adopted to control the MDPs, we discuss the existence and synthesis of policies that allow for perfect detection. We start with the case of two MDPs and establish a necessary and sufficient condition for the existence of policies that lead to perfect detection. Based on this condition, we then develop an algorithm that efficiently (in time polynomial in the size of the MDPs) determines the existence of policies and synthesizes one when they exist. We further extend the results to the more general case where there are more than two MDPs in the candidate set, and we develop a policy synthesis algorithm based on the breadth-first search and recursion. We demonstrate the effectiveness of our algorithms through numerical examples.

math.OC↗

arXiv2021

On-The-Fly Control of Unknown Systems: From Side Information to Performance Guarantees through Reachability

We develop data-driven algorithms for reachability analysis and control of systems with a priori unknown nonlinear dynamics. The resulting algorithms not only are suitable for settings with real-time requirements but also provide provable performance guarantees. To this end, they merge noisy data from only a single finite-horizon trajectory and, if available, various forms of side information. Such side information may include knowledge of the regularity of the dynamics, algebraic constraints on the states, monotonicity, or decoupling in the dynamics between the states. Specifically, we develop two algorithms, $\texttt{DaTaReach}$ and $\texttt{DaTaControl}$, to over-approximate the reachable set and design control signals for the system on the fly. $\texttt{DaTaReach}$ constructs a differential inclusion that contains the unknown dynamics. Then, in a discrete-time setting, it over-approximates the reachable set through interval Taylor-based methods applied to systems with dynamics described as differential inclusions. We provide a bound on the time step size that ensures the correctness and termination of $\texttt{DaTaReach}$. $\texttt{DaTaControl}$ enables convex-optimization-based control using the computed over-approximation and the receding-horizon control framework. Besides, $\texttt{DaTaControl}$ achieves near-optimal control and is suitable for real-time control of such systems. We establish a bound on its suboptimality and the number of primitive operations it requires to compute control values. Then, we theoretically show that $\texttt{DaTaControl}$ achieves tighter suboptimality bounds with an increasing amount of data and richer side information. Finally, experiments on a unicycle, quadrotor, and aircraft systems demonstrate the efficacy of both algorithms over existing approaches.

eess.SY↗

arXiv2021

Task-Guided Inverse Reinforcement Learning Under Partial Information

We study the problem of inverse reinforcement learning (IRL), where the learning agent recovers a reward function using expert demonstrations. Most of the existing IRL techniques make the often unrealistic assumption that the agent has access to full information about the environment. We remove this assumption by developing an algorithm for IRL in partially observable Markov decision processes (POMDPs). The algorithm addresses several limitations of existing techniques that do not take the information asymmetry between the expert and the learner into account. First, it adopts causal entropy as the measure of the likelihood of the expert demonstrations as opposed to entropy in most existing IRL techniques, and avoids a common source of algorithmic complexity. Second, it incorporates task specifications expressed in temporal logic into IRL. Such specifications may be interpreted as side information available to the learner a priori in addition to the demonstrations and may reduce the information asymmetry. Nevertheless, the resulting formulation is still nonconvex due to the intrinsic nonconvexity of the so-called forward problem, i.e., computing an optimal policy given a reward function, in POMDPs. We address this nonconvexity through sequential convex programming and introduce several extensions to solve the forward problem in a scalable manner. This scalability allows computing policies that incorporate memory at the expense of added computational cost yet also outperform memoryless policies. We demonstrate that, even with severely limited data, the algorithm learns reward functions and policies that satisfy the task and induce a similar behavior to the expert by leveraging the side information and incorporating memory into the policy.

cs.LG↗

arXiv2021

Proportional-Integral Projected Gradient Method for Conic Optimization

Conic optimization is the minimization of a differentiable convex objective function subject to conic constraints. We propose a novel primal-dual first-order method for conic optimization, named proportional-integral projected gradient method (PIPG). PIPG ensures that both the primal-dual gap and the constraint violation converge to zero at the rate of $O(1/k)$, where $k$ is the number of iterations. If the objective function is strongly convex, PIPG improves the convergence rate of the primal-dual gap to $O(1/k^2)$. Further, unlike any existing first-order methods, PIPG also improves the convergence rate of the constraint violation to $O(1/k^3)$. We demonstrate the application of PIPG in constrained optimal control problems.

math.OC↗

arXiv2021

A Barrier Pair Method for Safe Human-Robot Shared Autonomy

Shared autonomy provides a framework where a human and an automated system, such as a robot, jointly control the system's behavior, enabling an effective solution for various applications, including human-robot interaction. However, a challenging problem in shared autonomy is safety because the human input may be unknown and unpredictable, which affects the robot's safety constraints. If the human input is a force applied through physical contact with the robot, it also alters the robot's behavior to maintain safety. We address the safety issue of shared autonomy in real-time applications by proposing a two-layer control framework. In the first layer, we use the history of human input measurements to infer what the human wants the robot to do and define the robot's safety constraints according to that inference. In the second layer, we formulate a rapidly-exploring random tree of barrier pairs, with each barrier pair composed of a barrier function and a controller. Using the controllers in these barrier pairs, the robot is able to maintain its safe operation under the intervention from the human input. This proposed control framework allows the robot to assist the human while preventing them from encountering safety issues. We demonstrate the proposed control framework on a simulation of a two-linkage manipulator robot.

cs.RO↗

arXiv2021

Faster Non-Convex Federated Learning via Global and Local Momentum

We propose \texttt{FedGLOMO}, a novel federated learning (FL) algorithm with an iteration complexity of $\mathcal{O}(ε^{-1.5})$ to converge to an $ε$-stationary point (i.e., $\mathbb{E}[\|\nabla f(\bm{x})\|^2] \leq ε$) for smooth non-convex functions -- under arbitrary client heterogeneity and compressed communication -- compared to the $\mathcal{O}(ε^{-2})$ complexity of most prior works. Our key algorithmic idea that enables achieving this improved complexity is based on the observation that the convergence in FL is hampered by two sources of high variance: (i) the global server aggregation step with multiple local updates, exacerbated by client heterogeneity, and (ii) the noise of the local client-level stochastic gradients. By modeling the server aggregation step as a generalized gradient-type update, we propose a variance-reducing momentum-based global update at the server, which when applied in conjunction with variance-reduced local updates at the clients, enables \texttt{FedGLOMO} to enjoy an improved convergence rate. Moreover, we derive our results under a novel and more realistic client-heterogeneity assumption which we verify empirically -- unlike prior assumptions that are hard to verify. Our experiments illustrate the intrinsic variance reduction effect of \texttt{FedGLOMO}, which implicitly suppresses client-drift in heterogeneous data distribution settings and promotes communication efficiency.

stat.ML↗

arXiv2021

Algorithms for Fairness in Sequential Decision Making

It has recently been shown that if feedback effects of decisions are ignored, then imposing fairness constraints such as demographic parity or equality of opportunity can actually exacerbate unfairness. We propose to address this challenge by modeling feedback effects as Markov decision processes (MDPs). First, we propose analogs of fairness properties for the MDP setting. Second, we propose algorithms for learning fair decision-making policies for MDPs. Finally, we demonstrate the need to account for dynamical effects using simulations on a loan applicant MDP.

cs.LG↗

arXiv2021

Non-Parametric Neuro-Adaptive Control Subject to Task Specifications

We develop a learning-based algorithm for the control of autonomous systems governed by unknown, nonlinear dynamics to satisfy user-specified spatio-temporal tasks expressed as signal temporal logic specifications. Most existing algorithms either assume certain parametric forms for the unknown dynamic terms or resort to unnecessarily large control inputs in order to provide theoretical guarantees. The proposed algorithm addresses these drawbacks by integrating neural-network-based learning with adaptive control. More specifically, the algorithm learns a controller, represented as a neural network, using training data that correspond to a collection of system parameters and tasks. These parameters and tasks are derived by varying the nominal parameters and the spatio-temporal constraints of the user-specified task, respectively. It then incorporates this neural network into an online closed-form adaptive control policy in such a way that the resulting behavior satisfies the user-defined task. The proposed algorithm does not use any a priori information on the unknown dynamic terms or any approximation schemes. We provide formal theoretical guarantees on the satisfaction of the task. Numerical experiments on a robotic manipulator and a unicycle robot demonstrate that the proposed algorithm guarantees the satisfaction of 50 user-defined tasks, and outperforms control policies that do not employ online adaptation or the neural-network controller. Finally, we show that the proposed algorithm achieves greater performance than standard reinforcement-learning algorithms in the pendulum benchmarking environment.

cs.RO↗

arXiv2021

Adapting to the Behavior of Environments with Bounded Memory

We study the problem of synthesizing implementations from temporal logic specifications that need to work correctly in all environments that can be represented as transducers with a limited number of states. This problem was originally defined and studied by Kupferman, Lustig, Vardi, and Yannakakis. They provide NP and 2-EXPTIME lower and upper bounds (respectively) for the complexity of this problem, in the size of the transducer. We tighten the gap by providing a PSPACE lower bound, thereby showing that algorithms for solving this problem are unlikely to scale to large environment sizes. This result is somewhat unfortunate as solving this problem enables tackling some high-level control problems in which an agent has to infer the environment behavior from observations. To address this observation, we study a modified synthesis problem in which the synthesized controller must gather information about the environment's behavior safely. We show that the problem of determining whether the behavior of such an environment can be safely learned is only co-NP-complete. Furthermore, in such scenarios, the behavior of the environment can be learned using a Turing machine that requires at most polynomial space in the size of the environment's transducer.

cs.FL↗

arXiv2021

Deceptive Decision-Making Under Uncertainty

We study the design of autonomous agents that are capable of deceiving outside observers about their intentions while carrying out tasks in stochastic, complex environments. By modeling the agent's behavior as a Markov decision process, we consider a setting where the agent aims to reach one of multiple potential goals while deceiving outside observers about its true goal. We propose a novel approach to model observer predictions based on the principle of maximum entropy and to efficiently generate deceptive strategies via linear programming. The proposed approach enables the agent to exhibit a variety of tunable deceptive behaviors while ensuring the satisfaction of probabilistic constraints on the behavior. We evaluate the performance of the proposed approach via comparative user studies and present a case study on the streets of Manhattan, New York, using real travel time distributions.

cs.AI↗

arXiv2021

Proportional-Integral Projected Gradient Method for Infeasibility Detection in Conic Optimization

A constrained optimization problem is primal infeasible if its constraints cannot be satisfied, and dual infeasible if the constraints of its dual problem cannot be satisfied. We propose a novel iterative method, named proportional-integral projected gradient method (PIPG), for detecting primal and dual infeasiblity in convex optimization with quadratic objective function and conic constraints. The iterates of PIPG either asymptotically provide a proof of primal or dual infeasibility, or asymptotically satisfy a set of primal-dual optimality conditions. Unlike existing methods, PIPG does not compute matrix inverse, which makes it better suited for large-scale and real-time applications. We demonstrate the application of PIPG in quasiconvex and mixed-integer optimization using examples in constrained optimal control.

math.OC↗

arXiv2021

Simultaneous Perception-Action Design via Invariant Finite Belief Sets

Although perception is an increasingly dominant portion of the overall computational cost for autonomous systems, only a fraction of the information perceived is likely to be relevant to the current task. To alleviate these perception costs, we develop a novel simultaneous perception-action design framework wherein an agent senses only the task-relevant information. This formulation differs from that of a partially observable Markov decision process, since the agent is free to synthesize not only its policy for action selection but also its belief-dependent observation function. The method enables the agent to balance its perception costs with those incurred by operating in its environment. To obtain a computationally tractable solution, we approximate the value function using a novel method of invariant finite belief sets, wherein the agent acts exclusively on a finite subset of the continuous belief space. We solve the approximate problem through value iteration in which a linear program is solved individually for each belief state in the set, in each iteration. Finally, we prove that the value functions, under an assumption on their structure, converge to their continuous state-space values as the sample density increases.

cs.AI↗

arXiv2021

From Agile Ground to Aerial Navigation: Learning from Learned Hallucination

This paper presents a self-supervised Learning from Learned Hallucination (LfLH) method to learn fast and reactive motion planners for ground and aerial robots to navigate through highly constrained environments. The recent Learning from Hallucination (LfH) paradigm for autonomous navigation executes motion plans by random exploration in completely safe obstacle-free spaces, uses hand-crafted hallucination techniques to add imaginary obstacles to the robot's perception, and then learns motion planners to navigate in realistic, highly-constrained, dangerous spaces. However, current hand-crafted hallucination techniques need to be tailored for specific robot types (e.g., a differential drive ground vehicle), and use approximations heavily dependent on certain assumptions (e.g., a short planning horizon). In this work, instead of manually designing hallucination functions, LfLH learns to hallucinate obstacle configurations, where the motion plans from random exploration in open space are optimal, in a self-supervised manner. LfLH is robust to different robot types and does not make assumptions about the planning horizon. Evaluated in both simulated and physical environments with a ground and an aerial robot, LfLH outperforms or performs comparably to previous hallucination approaches, along with sampling- and optimization-based classical methods.

cs.RO↗

arXiv2021

Generalization Bounds for Sparse Random Feature Expansions

Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent similar function spaces without a costly training phase. However, for accuracy, random feature methods require more measurements than trainable parameters, limiting their use for data-scarce applications or problems in scientific machine learning. This paper introduces the sparse random feature expansion to obtain parsimonious random feature models. Specifically, we leverage ideas from compressive sensing to generate random feature expansions with theoretical guarantees even in the data-scarce setting. In particular, we provide generalization bounds for functions in a certain class (that is dense in a reproducing kernel Hilbert space) depending on the number of samples and the distribution of features. The generalization bounds improve with additional structural conditions, such as coordinate sparsity, compact clusters of the spectrum, or rapid spectral decay. In particular, by introducing sparse features, i.e. features with random sparse weights, we provide improved bounds for low order functions. We show that the sparse random feature expansions outperforms shallow networks in several scientific machine learning tasks.

stat.ML↗

arXiv2021

Self-Supervised Online Reward Shaping in Sparse-Reward Environments

We introduce Self-supervised Online Reward Shaping (SORS), which aims to improve the sample efficiency of any RL algorithm in sparse-reward environments by automatically densifying rewards. The proposed framework alternates between classification-based reward inference and policy update steps -- the original sparse reward provides a self-supervisory signal for reward inference by ranking trajectories that the agent observes, while the policy update is performed with the newly inferred, typically dense reward function. We introduce theory that shows that, under certain conditions, this alteration of the reward function will not change the optimal policy of the original MDP, while potentially increasing learning speed significantly. Experimental results on several sparse-reward environments demonstrate that, across multiple domains, the proposed algorithm is not only significantly more sample efficient than a standard RL baseline using sparse rewards, but, at times, also achieves similar sample efficiency compared to when hand-designed dense reward functions are used.

cs.LG↗

arXiv2021

Byzantine-Resilient Distributed Hypothesis Testing With Time-Varying Network Topology

We study the problem of distributed hypothesis testing over a network of mobile agents with limited communication and sensing ranges to infer the true hypothesis collaboratively. In particular, we consider a scenario where there is an unknown subset of compromised agents that may deliberately share altered information to undermine the team objective. We propose two distributed algorithms where each agent maintains and updates two sets of beliefs (i.e., probability distributions over the hypotheses), namely local and actual beliefs (LB and AB respectively for brevity). In both algorithms, at every time step, each agent shares its AB with other agents within its communication range and makes a local observation to update its LB. Then both algorithms can use the shared information to update ABs under certain conditions. One requires receiving a certain number of shared ABs at each time instant; the other accumulates shared ABs over time and updates after the number of shared ABs exceeds a prescribed threshold. Otherwise, both algorithms rely on the agent's current LB and AB to update the new AB. We prove under mild assumptions that the AB for every non-compromised agent converges almost surely to the true hypothesis, without requiring connectivity in the underlying time-varying network topology. Using a simulation of a team of unmanned aerial vehicles aiming to classify adversarial agents among themselves, we illustrate and compare the proposed algorithms. Finally, we show experimentally that the second algorithm consistently outperforms the first algorithm in terms of the speed of convergence.

eess.SY↗

arXiv2021

Active Finite Reward Automaton Inference and Reinforcement Learning Using Queries and Counterexamples

Despite the fact that deep reinforcement learning (RL) has surpassed human-level performances in various tasks, it still has several fundamental challenges. First, most RL methods require intensive data from the exploration of the environment to achieve satisfactory performance. Second, the use of neural networks in RL renders it hard to interpret the internals of the system in a way that humans can understand. To address these two challenges, we propose a framework that enables an RL agent to reason over its exploration process and distill high-level knowledge for effectively guiding its future explorations. Specifically, we propose a novel RL algorithm that learns high-level knowledge in the form of a finite reward automaton by using the L* learning algorithm. We prove that in episodic RL, a finite reward automaton can express any non-Markovian bounded reward functions with finitely many reward values and approximate any non-Markovian bounded reward function (with infinitely many reward values) with arbitrary precision. We also provide a lower bound for the episode length such that the proposed RL approach almost surely converges to an optimal policy in the limit. We test this approach on two RL environments with non-Markovian reward functions, choosing a variety of tasks with increasing complexity for each environment. We compare our algorithm with the state-of-the-art RL algorithms for non-Markovian reward functions, such as Joint Inference of Reward machines and Policies for RL (JIRP), Learning Reward Machine (LRM), and Proximal Policy Optimization (PPO2). Our results show that our algorithm converges to an optimal policy faster than other baseline methods.

cs.LG↗