arXiv subjects

Ufuk Topcu

Publications and source records attributed to Ufuk Topcu.

At least 289 records · Page 16Linked to original sources

arXiv2019

The Dirichlet Mechanism for Differential Privacy on the Unit Simplex

As members of a network share more information with each other and network providers, sensitive data leakage raises privacy concerns. To address this need for a class of problems, we introduce a novel mechanism that privatizes vectors belonging to the unit simplex. Such vectors can be seen in many applications, such as privatizing a decision-making policy in a Markov decision process. We use differential privacy as the underlying mathematical framework for these developments. The introduced mechanism is a probabilistic mapping that maps a vector within the unit simplex to the same domain according to a Dirichlet distribution. We find the mechanism well-suited for inputs within the unit simplex because it always returns a privatized output that is also in the unit simplex. Therefore, no further projection back onto the unit simplex is required. We verify the privacy guarantees of the mechanism for two cases, namely, identity queries and average queries. In the former case, we derive expressions for the differential privacy level of privatizing a single vector within the unit simplex. In the latter case, we study the mechanism for privatizing the average of a collection of vectors, each of which is in the unit simplex. We establish a trade-off between the strength of privacy and the variance of the mechanism output, and we introduce a parameter to balance the trade-off between them. Numerical results illustrate these developments.

cs.CR↗

arXiv2019

Differentially Private Controller Synthesis With Metric Temporal Logic Specifications

Privacy is an important concern in various multiagent systems in which data collected from the agents are sensitive. We propose a differentially private controller synthesis approach for multi-agent systems subject to high-level specifications expressed in metric temporal logic (MTL). We consider a setting where each agent sends data to a cloud (computing station) through a set of local hubs and the cloud is responsible for computing the control inputs of the agents. Specifically, each agent adds privacy noise (e.g., Gaussian noise) point-wise in time to its own outputs before sharing them with a local hub. Each local hub runs a Kalman filter to estimate the state of the corresponding agent and periodically sends such state estimates to the cloud. The cloud computes the optimal inputs for each agent subject to an MTL specification. While guaranteeing differential privacy of each agent, the controller is also synthesized to ensure a probabilistic guarantee for satisfying the MTL specification.We provide an implementation of the proposed method on a simulation case study with two Baxter-On-Wheels robots as the agents.

eess.SY↗

arXiv2019

Controller Synthesis for Multi-Agent Systems With Intermittent Communication: A Metric Temporal Logic Approach

This paper develops a controller synthesis approach for a multi-agent system (MAS) with intermittent communication. We adopt a leader-follower scheme, where a mobile leader with absolute position sensors switches among a set of followers without absolute position sensors to provide each follower with intermittent state information.We model the MAS as a switched system. The followers are to asymptotically reach a predetermined consensus state. To guarantee the stability of the switched system and the consensus of the followers, we derive maximum and minimal dwell-time conditions to constrain the intervals between consecutive time instants at which the leader should provide state information to the same follower. Furthermore, the leader needs to satisfy practical constraints such as charging its battery and staying in specific regions of interest. Both the maximum and minimum dwell-time conditions and these practical constraints can be expressed by metric temporal logic (MTL) specifications. We iteratively compute the optimal control inputs such that the leader satisfies the MTL specifications, while guaranteeing stability and consensus of the followers. We implement the proposed method on a case study with three mobile robots as the followers and one quadrotor as the leader.

eess.SY↗

arXiv2019

Unpredictable Planning Under Partial Observability

We study the problem of synthesizing a controller that maximizes the entropy of a partially observable Markov decision process (POMDP) subject to a constraint on the expected total reward. Such a controller minimizes the predictability of a decision-maker's trajectories while guaranteeing the completion of a task expressed by a reward function. First, we prove that a decision-maker with perfect observations can randomize its paths at least as well as a decision-maker with partial observations. Then, focusing on finite-state controllers, we recast the entropy maximization problem as a so-called parameter synthesis problem for a parametric Markov chain (pMC). We show that the maximum entropy of a POMDP is lower bounded by the maximum entropy of this pMC. Finally, we present an algorithm, based on a nonlinear optimization problem, to synthesize an FSC that locally maximizes the entropy of a POMDP over FSCs with the same number of memory states. In numerical examples, we demonstrate the proposed algorithm on motion planning scenarios.

math.OC↗

arXiv2019

Transfer of Temporal Logic Formulas in Reinforcement Learning

Transferring high-level knowledge from a source task to a target task is an effective way to expedite reinforcement learning (RL). For example, propositional logic and first-order logic have been used as representations of such knowledge. We study the transfer of knowledge between tasks in which the timing of the events matters. We call such tasks temporal tasks. We concretize similarity between temporal tasks through a notion of logical transferability, and develop a transfer learning approach between different yet similar temporal tasks. We first propose an inference technique to extract metric interval temporal logic (MITL) formulas in sequential disjunctive normal form from labeled trajectories collected in RL of the two tasks. If logical transferability is identified through this inference, we construct a timed automaton for each sequential conjunctive subformula of the inferred MITL formulas from both tasks. We perform RL on the extended state which includes the locations and clock valuations of the timed automata for the source task. We then establish mappings between the corresponding components (clocks, locations, etc.) of the timed automata from the two tasks, and transfer the extended Q-functions based on the established mappings. Finally, we perform RL on the extended state for the target task, starting with the transferred extended Q-functions. Our results in two case studies show, depending on how similar the source task and the target task are, that the sampling efficiency for the target task can be improved by up to one order of magnitude by performing RL in the extended state space, and further improved by up to another order of magnitude using the transferred extended Q-functions.

cs.AI↗

arXiv2019

Barrier Certificates for Assured Machine Teaching

Machine teaching can be viewed as optimal control for learning. Given a learner's model, machine teaching aims to determine the optimal training data to steer the learner towards a target hypothesis. In this paper, we are interested in providing assurances for machine teaching algorithms using control theory. In particular, we study a well-established learner's model in the machine teaching literature that is captured by the local preference over a version space. We interpret the problem of teaching a preference-based learner as solving a partially observable Markov decision process (POMDP). We then show that the POMDP formulation can be cast as a special hybrid system, i.e., a discrete-time switched system. Subsequently, we use barrier certificates to verify set-theoric properties of this special hybrid system. We show how the computation of the barrier certificate can be decomposed and numerically implemented as the solution to a sum-of-squares (SOS) program. For illustration, we show how the proposed framework based on control theory can be used to verify the teaching performance of two well-known machine teaching methods.

eess.SY↗

arXiv2019

Entropy-Regularized Stochastic Games

In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have perfect information about the stochastic transition model of the environment. However, implementing such strategies may make the players vulnerable to unforeseen changes in the environment. In this paper, we introduce entropy-regularized stochastic games where each player aims to maximize the causal entropy of its strategy in addition to its expected payoff. The regularization term balances each player's rationality with its belief about the level of misinformation about the transition model. We consider both entropy-regularized $N$-stage and entropy-regularized discounted stochastic games, and establish the existence of a value in both games. Moreover, we prove the sufficiency of Markovian and stationary mixed strategies to attain the value, respectively, in $N$-stage and discounted games. Finally, we present algorithms, which are based on convex optimization problems, to compute the optimal strategies. In a numerical example, we demonstrate the proposed method on a motion planning scenario and illustrate the effect of the regularization term on the expected payoff.

math.OC↗

arXiv2019

An Encoder-Decoder Based Approach for Anomaly Detection with Application in Additive Manufacturing

We present a novel unsupervised deep learning approach that utilizes the encoder-decoder architecture for detecting anomalies in sequential sensor data collected during industrial manufacturing. Our approach is designed not only to detect whether there exists an anomaly at a given time step, but also to predict what will happen next in the (sequential) process. We demonstrate our approach on a dataset collected from a real-world testbed. The dataset contains images collected under both normal conditions and synthetic anomalies. We show that the encoder-decoder model is able to identify the injected anomalies in a modern manufacturing process in an unsupervised fashion. In addition, it also gives hints about the temperature non-uniformity of the testbed during manufacturing, which is what we are not aware of before doing the experiment.

cs.LG↗

arXiv2019

Entropy Maximization for Markov Decision Processes Under Temporal Logic Constraints

We study the problem of synthesizing a policy that maximizes the entropy of a Markov decision process (MDP) subject to a temporal logic constraint. Such a policy minimizes the predictability of the paths it generates, or dually, maximizes the exploration of different paths in an MDP while ensuring the satisfaction of a temporal logic specification. We first show that the maximum entropy of an MDP can be finite, infinite or unbounded. We provide necessary and sufficient conditions under which the maximum entropy of an MDP is finite, infinite or unbounded. We then present an algorithm which is based on a convex optimization problem to synthesize a policy that maximizes the entropy of an MDP. We also show that maximizing the entropy of an MDP is equivalent to maximizing the entropy of the paths that reach a certain set of states in the MDP. Finally, we extend the algorithm to an MDP subject to a temporal logic specification. In numerical examples, we demonstrate the proposed method on different motion planning scenarios and illustrate the relation between the restrictions imposed on the paths by a specification, the maximum entropy, and the predictability of paths.

math.OC↗

arXiv2019

Strategy Synthesis in POMDPs via Game-Based Abstractions

We study synthesis problems with constraints in partially observable Markov decision processes (POMDPs), where the objective is to compute a strategy for an agent that is guaranteed to satisfy certain safety and performance specifications. Verification and strategy synthesis for POMDPs are, however, computationally intractable in general. We alleviate this difficulty by focusing on planning applications and exploiting typical structural properties of such scenarios; for instance, we assume that the agent has the ability to observe its own position inside an environment. We propose an abstraction refinement framework which turns such a POMDP model into a (fully observable) probabilistic two-player game (PG). For the obtained PGs, efficient verification and synthesis tools allow to determine strategies with optimal safety and performance measures, which approximate optimal schedulers on the POMDP. If the approximation is too coarse to satisfy the given specifications, an refinement scheme improves the computed strategies. As a running example, we use planning problems where an agent moves inside an environment with randomly moving obstacles and restricted observability. We demonstrate that the proposed method advances the state of the art by solving problems several orders-of-magnitude larger than those that can be handled by existing POMDP solvers. Furthermore, this method gives guarantees on safety constraints, which is not supported by the majority of the existing solvers.

cs.RO↗

arXiv2019

Submodular Observation Selection and Information Gathering for Quadratic Models

We study the problem of selecting most informative subset of a large observation set to enable accurate estimation of unknown parameters. This problem arises in a variety of settings in machine learning and signal processing including feature selection, phase retrieval, and target localization. Since for quadratic measurement models the moment matrix of the optimal estimator is generally unknown, majority of prior work resorts to approximation techniques such as linearization of the observation model to optimize the alphabetical optimality criteria of an approximate moment matrix. Conversely, by exploiting a connection to the classical Van Trees' inequality, we derive new alphabetical optimality criteria without distorting the relational structure of the observation model. We further show that under certain conditions on parameters of the problem these optimality criteria are monotone and (weak) submodular set functions. These results enable us to develop an efficient greedy observation selection algorithm uniquely tailored for quadratic models, and provide theoretical bounds on its achievable utility.

eess.SP↗

arXiv2019

Control Theory Meets POMDPs: A Hybrid Systems Approach

Partially observable Markov decision processes (POMDPs) provide a modeling framework for a variety of sequential decision making under uncertainty scenarios in artificial intelligence (AI). Since the states are not directly observable in a POMDP, decision making has to be performed based on the output of a Bayesian filter (continuous beliefs). Hence, POMDPs are often computationally intractable to solve exactly and researchers resort to approximate methods often using discretizations of the continuous belief space. These approximate solutions are, however, prone to discretization errors, which has made POMDPs ineffective in applications, wherein guarantees for safety, optimality, or performance are required. To overcome the complexity challenge of POMDPs, we apply notions from control theory. The goal is to determine the reachable belief space of a POMDP, that is, the set of all possible evolutions given an initial belief distribution over the states and a set of actions and observations. We begin by casting the problem of analyzing a POMDP into analyzing the behavior of a discrete-time switched system. For estimating the reachable belief space, we find over-approximations in terms of sub-level sets of Lyapunov functions. Furthermore, in order to verify safety and optimality requirements of a given POMDP, we formulate a barrier certificate theorem, wherein we show that if there exists a barrier certificate satisfying a set of inequalities along with the belief update equation of the POMDP, the safety and optimality properties are guaranteed to hold. In both cases, we show how the calculations can be decomposed into smaller problems that can be solved in parallel. The conditions we formulate can be computationally implemented as a set of sum-of-squares programs. We illustrate the applicability of our method by addressing two problems in active ad scheduling and machine teaching.

eess.SY↗

arXiv2019

Synthesis of Provably Correct Autonomy Protocols for Shared Control

We synthesize shared control protocols subject to probabilistic temporal logic specifications. More specifically, we develop a framework in which a human and an autonomy protocol can issue commands to carry out a certain task. We blend these commands into a joint input to a robot. We model the interaction between the human and the robot as a Markov decision process (MDP) that represents the shared control scenario. Using inverse reinforcement learning, we obtain an abstraction of the human's behavior and decisions. We use randomized strategies to account for randomness in human's decisions, caused by factors such as complexity of the task specifications or imperfect interfaces. We design the autonomy protocol to ensure that the resulting robot behavior satisfies given safety and performance specifications in probabilistic temporal logic. Additionally, the resulting strategies generate behavior as similar to the behavior induced by the human's commands as possible. We solve the underlying problem efficiently using quasiconvex programming. Case studies involving autonomous wheelchair navigation and unmanned aerial vehicle mission planning showcase the applicability of our approach.

cs.RO↗

arXiv2019

Reward-Based Deception with Cognitive Bias

Deception plays a key role in adversarial or strategic interactions for the purpose of self-defence and survival. This paper introduces a general framework and solution to address deception. Most existing approaches for deception consider obfuscating crucial information to rational adversaries with abundant memory and computation resources. In this paper, we consider deceiving adversaries with bounded rationality and in terms of expected rewards. This problem is commonly encountered in many applications especially involving human adversaries. Leveraging the cognitive bias of humans in reward evaluation under stochastic outcomes, we introduce a framework to optimally assign resources of a limited quantity to optimally defend against human adversaries. Modeling such cognitive biases follows the so-called prospect theory from behavioral psychology literature. Then we formulate the resource allocation problem as a signomial program to minimize the defender's cost in an environment modeled as a Markov decision process. We use police patrol hour assignment as an illustrative example and provide detailed simulation results based on real-world data.

cs.AI↗

arXiv2019

Switched Linear Systems Meet Markov Decision Processes: Stability Guaranteed Policy Synthesis

Switched linear systems are time-varying nonlinear systems whose dynamics switch between different modes, where each mode corresponds to different linear dynamics. They arise naturally to model unexpected failures, environment uncertainties or system noises during system operation. In this paper, we consider a special class of switched linear systems where the mode switches are governed by Markov decision processes (MDPs). We study the problem of synthesizing a policy in an MDP that stabilizes the switched system. Given a policy, the switched linear system becomes a Markov jump linear system whose stability conditions have been extensively studied. We make use of these stability conditions and propose three different computation approaches to find the stabilizing policy in an MDP. We derive our first approach by extending the stability conditions for a Markov jump linear system to handle switches governed by an MDP. This approach requires finding a feasible solution of a set of bilinear matrix inequalities, which makes policy synthesis typically challenging. To improve scalability, we provide two approaches based on convex optimization. We give three examples to show and compare our proposed solutions.

math.OC↗

arXiv2019

Synthesis of Admissible Shields

Shield synthesis is an approach to enforce a set of safety-critical properties of a reactive system at runtime. A shield monitors the system and corrects any erroneous output values instantaneously. The shield deviates from the given outputs as little as it can and recovers to hand back control to the system as soon as possible. This paper takes its inspiration from a case study on mission planning for unmanned aerial vehicles (UAVs) in which k-stabilizing shields, which guarantee recovery in a finite time, could not be constructed. We introduce the notion of admissible shields, which improves k-stabilizing shields in two ways: (1) whereas k-stabilizing shields take an adversarial view on the system, admissible shields take a collaborative view. That is, if there is no shield that guarantees recovery within k steps regardless of system behavior, the admissible shield will attempt to work with the system to recover as soon as possible. (2) Admissible shields can handle system failures during the recovery phase. In our experimental results we show that for UAVs, we can generate admissible shields, even when k-stabilizing shields do not exist.

cs.LO↗

arXiv2019

Graph Temporal Logic Inference for Classification and Identification

Inferring spatial-temporal properties from data is important for many complex systems, such as additive manufacturing systems, swarm robotic systems and biological networks. Such systems can often be modeled as a labeled graph where labels on the nodes and edges represent relevant measurements such as temperatures and distances. We introduce graph temporal logic (GTL) which can express properties such as "whenever a node's label is above 10, for the next 3 time units there are always at least two neighboring nodes with an edge label of at most 2 where the node labels are above 5". This paper is a first attempt to infer spatial (graph) temporal logic formulas from data for classification and identification. For classification, we infer a GTL formula that classifies two sets of graph temporal trajectories with minimal misclassification rate. For identification, we infer a GTL formula that is informative and is satisfied by the graph temporal trajectories in the dataset with high probability. The informativeness of a GTL formula is measured by the information gain with respect to given prior knowledge represented by a prior probability distribution. We implement the proposed approach to classify the graph patterns of tensile specimens built from selective laser sintering (SLS) process with varying strengths, and to identify informative spatial-temporal patterns from experimental data of the SLS cooldown process and simulation data of a swarm of robots.

cs.LO↗

arXiv2019

Counterexample-Guided Strategy Improvement for POMDPs Using Recurrent Neural Networks

We study strategy synthesis for partially observable Markov decision processes (POMDPs). The particular problem is to determine strategies that provably adhere to (probabilistic) temporal logic constraints. This problem is computationally intractable and theoretically hard. We propose a novel method that combines techniques from machine learning and formal verification. First, we train a recurrent neural network (RNN) to encode POMDP strategies. The RNN accounts for memory-based decisions without the need to expand the full belief space of a POMDP. Secondly, we restrict the RNN-based strategy to represent a finite-memory strategy and implement it on a specific POMDP. For the resulting finite Markov chain, efficient formal verification techniques provide provable guarantees against temporal logic specifications. If the specification is not satisfied, counterexamples supply diagnostic information. We use this information to improve the strategy by iteratively training the RNN. Numerical experiments show that the proposed method elevates the state of the art in POMDP solving by up to three orders of magnitude in terms of solving times and model sizes.

cs.AI↗