arXiv subjects

Ufuk Topcu

Publications and source records attributed to Ufuk Topcu.

At least 181 records · Page 10Linked to original sources

arXiv2023

Learning Interpretable Temporal Properties from Positive Examples Only

We consider the problem of explaining the temporal behavior of black-box systems using human-interpretable models. To this end, based on recent research trends, we rely on the fundamental yet interpretable models of deterministic finite automata (DFAs) and linear temporal logic (LTL) formulas. In contrast to most existing works for learning DFAs and LTL formulas, we rely on only positive examples. Our motivation is that negative examples are generally difficult to observe, in particular, from black-box systems. To learn meaningful models from positive examples only, we design algorithms that rely on conciseness and language minimality of models as regularizers. To this end, our algorithms adopt two approaches: a symbolic and a counterexample-guided one. While the symbolic approach exploits an efficient encoding of language minimality as a constraint satisfaction problem, the counterexample-guided one relies on generating suitable negative examples to prune the search. Both the approaches provide us with effective algorithms with theoretical guarantees on the learned models. To assess the effectiveness of our algorithms, we evaluate all of them on synthetic data.

cs.LO↗

arXiv2023

Learning Sparse Control Tasks from Pixels by Latent Nearest-Neighbor-Guided Explorations

Recent progress in deep reinforcement learning (RL) and computer vision enables artificial agents to solve complex tasks, including locomotion, manipulation and video games from high-dimensional pixel observations. However, domain specific reward functions are often engineered to provide sufficient learning signals, requiring expert knowledge. While it is possible to train vision-based RL agents using only sparse rewards, additional challenges in exploration arise. We present a novel and efficient method to solve sparse-reward robot manipulation tasks from only image observations by utilizing a few demonstrations. First, we learn an embedded neural dynamics model from demonstration transitions and further fine-tune it with the replay buffer. Next, we reward the agents for staying close to the demonstrated trajectories using a distance metric defined in the embedding space. Finally, we use an off-policy, model-free vision RL algorithm to update the control policies. Our method achieves state-of-the-art sample efficiency in simulation and enables efficient training of a real Franka Emika Panda manipulator.

cs.RO↗

arXiv2023

Joint Learning of Reward Machines and Policies in Environments with Partially Known Semantics

We study the problem of reinforcement learning for a task encoded by a reward machine. The task is defined over a set of properties in the environment, called atomic propositions, and represented by Boolean variables. One unrealistic assumption commonly used in the literature is that the truth values of these propositions are accurately known. In real situations, however, these truth values are uncertain since they come from sensors that suffer from imperfections. At the same time, reward machines can be difficult to model explicitly, especially when they encode complicated tasks. We develop a reinforcement-learning algorithm that infers a reward machine that encodes the underlying task while learning how to execute it, despite the uncertainties of the propositions' truth values. In order to address such uncertainties, the algorithm maintains a probabilistic estimate about the truth value of the atomic propositions; it updates this estimate according to new sensory measurements that arrive from the exploration of the environment. Additionally, the algorithm maintains a hypothesis reward machine, which acts as an estimate of the reward machine that encodes the task to be learned. As the agent explores the environment, the algorithm updates the hypothesis reward machine according to the obtained rewards and the estimate of the atomic propositions' truth value. Finally, the algorithm uses a Q-learning procedure for the states of the hypothesis reward machine to determine the policy that accomplishes the task. We prove that the algorithm successfully infers the reward machine and asymptotically learns a policy that accomplishes the respective task.

cs.LG↗

arXiv2023

Differential Privacy in Cooperative Multiagent Planning

Privacy-aware multiagent systems must protect agents' sensitive data while simultaneously ensuring that agents accomplish their shared objectives. Towards this goal, we propose a framework to privatize inter-agent communications in cooperative multiagent decision-making problems. We study sequential decision-making problems formulated as cooperative Markov games with reach-avoid objectives. We apply a differential privacy mechanism to privatize agents' communicated symbolic state trajectories, and then we analyze tradeoffs between the strength of privacy and the team's performance. For a given level of privacy, this tradeoff is shown to depend critically upon the total correlation among agents' state-action processes. We synthesize policies that are robust to privacy by reducing the value of the total correlation. Numerical experiments demonstrate that the team's performance under these policies decreases by only 3 percent when comparing private versus non-private implementations of communication. By contrast, the team's performance decreases by roughly 86 percent when using baseline policies that ignore total correlation and only optimize team performance.

cs.MA↗

arXiv2023

Temporal-Logic-Based Reward Shaping for Continuing Reinforcement Learning Tasks

In continuing tasks, average-reward reinforcement learning may be a more appropriate problem formulation than the more common discounted reward formulation. As usual, learning an optimal policy in this setting typically requires a large amount of training experiences. Reward shaping is a common approach for incorporating domain knowledge into reinforcement learning in order to speed up convergence to an optimal policy. However, to the best of our knowledge, the theoretical properties of reward shaping have thus far only been established in the discounted setting. This paper presents the first reward shaping framework for average-reward learning and proves that, under standard assumptions, the optimal policy under the original reward function can be recovered. In order to avoid the need for manual construction of the shaping function, we introduce a method for utilizing domain knowledge expressed as a temporal logic formula. The formula is automatically translated to a shaping function that provides additional reward throughout the learning process. We evaluate the proposed method on three continuing tasks. In all cases, shaping speeds up the average-reward learning rate without any reduction in the performance of the learned policy compared to relevant baselines.

cs.AI↗

arXiv2023

Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control

Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in real-world scenarios where only limited observations of the system are available. Furthermore, purely data-driven methods often neglect useful a priori knowledge, such as approximate models of the system dynamics. We present a method to incorporate such prior knowledge into data-driven control algorithms using kernel embeddings, a nonparametric machine learning technique based in the theory of reproducing kernel Hilbert spaces. Our proposed approach incorporates prior knowledge of the system dynamics as a bias term in the kernel learning problem. We formulate the biased learning problem as a least-squares problem with a regularization term that is informed by the dynamics, that has an efficiently computable, closed-form solution. Through numerical experiments, we empirically demonstrate the improved sample efficiency and out-of-sample generalization of our approach over a purely data-driven baseline. We demonstrate an application of our method to control through a target tracking problem with nonholonomic dynamics, and on spring-mass-damper and F-16 aircraft state prediction tasks.

eess.SY↗

arXiv2023

Constrained Active Classification Using Partially Observable Markov Decision Processes

In this work, we study the problem of actively classifying the attributes of dynamical systems characterized as a finite set of Markov decision process (MDP) models. We are interested in finding strategies that actively interact with the dynamical system and observe its reactions so that the attribute of interest is classified efficiently with high confidence. We present a decision-theoretic framework based on partially observable Markov decision processes (POMDPs). The proposed framework relies on assigning a classification belief (a probability distribution) to the attributes of interest. Given an initial belief, a confidence level over which a classification decision can be made, a cost bound, safe belief sets, and a finite time horizon, we compute POMDP strategies leading to classification decisions. We present three different algorithms to compute such strategies. The first algorithm computes the optimal strategy exactly by value iteration. To overcome the computational complexity of computing the exact solutions, we propose a second algorithm based on adaptive sampling and a third based on a Monte Carlo tree search to approximate the optimal probability of reaching a classification decision. We illustrate the proposed methodology using examples from medical diagnosis, security surveillance, and wildlife classification.

eess.SY↗

arXiv2023

Deception in Supervisory Control

The use of deceptive strategies is important for an agent that attempts not to reveal his intentions in an adversarial environment. We consider a setting in which a supervisor provides a reference policy and expects an agent to follow the reference policy and perform a task. The agent may instead follow a different, deceptive policy to achieve a different task. We model the environment and the behavior of the agent with a Markov decision process, represent the tasks of the agent and the supervisor with reachability specifications, and study the synthesis of optimal deceptive policies for such agents. We also study the synthesis of optimal reference policies that prevent deceptive strategies of the agent and achieve the supervisor's task with high probability. We show that the synthesis of optimal deceptive policies has a convex optimization problem formulation, while the synthesis of optimal reference policies requires solving a nonconvex optimization problem. We also show that the synthesis of optimal reference policies is NP-hard.

math.OC↗

arXiv2022

Task-Guided IRL in POMDPs that Scales

In inverse reinforcement learning (IRL), a learning agent infers a reward function encoding the underlying task using demonstrations from experts. However, many 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). We address two limitations of existing IRL techniques. First, they require an excessive amount of data due to the information asymmetry between the expert and the learner. Second, most of these IRL techniques require solving the computationally intractable forward problem -- computing an optimal policy given a reward function -- in POMDPs. The developed algorithm reduces the information asymmetry while increasing the data efficiency by incorporating 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. Further, the algorithm avoids a common source of algorithmic complexity by building on causal entropy as the measure of the likelihood of the demonstrations as opposed to entropy. Nevertheless, the resulting problem is nonconvex due to the so-called forward problem. We solve the intrinsic nonconvexity of the forward problem in a scalable manner through a sequential linear programming scheme that guarantees to converge to a locally optimal policy. In a series of examples, including experiments in a high-fidelity Unity simulator, we demonstrate that even with a limited amount of data and POMDPs with tens of thousands of states, our algorithm learns reward functions and policies that satisfy the task while inducing similar behavior to the expert by leveraging the provided side information.

cs.LG↗

arXiv2022

Taylor-Lagrange Neural Ordinary Differential Equations: Toward Fast Training and Evaluation of Neural ODEs

Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every forward evaluation of a NODE requires numerical integration of the neural network used to capture the system dynamics, making their training prohibitively expensive. Existing works rely on off-the-shelf adaptive step-size numerical integration schemes, which often require an excessive number of evaluations of the underlying dynamics network to obtain sufficient accuracy for training. By contrast, we accelerate the evaluation and the training of NODEs by proposing a data-driven approach to their numerical integration. The proposed Taylor-Lagrange NODEs (TL-NODEs) use a fixed-order Taylor expansion for numerical integration, while also learning to estimate the expansion's approximation error. As a result, the proposed approach achieves the same accuracy as adaptive step-size schemes while employing only low-order Taylor expansions, thus greatly reducing the computational cost necessary to integrate the NODE. A suite of numerical experiments, including modeling dynamical systems, image classification, and density estimation, demonstrate that TL-NODEs can be trained more than an order of magnitude faster than state-of-the-art approaches, without any loss in performance.

cs.LG↗

arXiv2022

Alternating Direction Method of Multipliers for Decomposable Saddle-Point Problems

Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of multipliers to such saddle-point problems. Instead of solving the original saddle-point problem directly, this algorithm solves smaller saddle-point problems by exploiting the decomposable structure. We show the convergence of this algorithm for convex-concave saddle-point problems under a mild assumption. We also provide a sufficient condition for which the assumption holds. We demonstrate the convergence properties of the saddle-point alternating direction method of multipliers with numerical examples on a power allocation problem in communication channels and a network routing problem with adversarial costs.

math.OC↗

arXiv2022

Class-Aware Adversarial Transformers for Medical Image Segmentation

Transformers have made remarkable progress towards modeling long-range dependencies within the medical image analysis domain. However, current transformer-based models suffer from several disadvantages: (1) existing methods fail to capture the important features of the images due to the naive tokenization scheme; (2) the models suffer from information loss because they only consider single-scale feature representations; and (3) the segmentation label maps generated by the models are not accurate enough without considering rich semantic contexts and anatomical textures. In this work, we present CASTformer, a novel type of adversarial transformers, for 2D medical image segmentation. First, we take advantage of the pyramid structure to construct multi-scale representations and handle multi-scale variations. We then design a novel class-aware transformer module to better learn the discriminative regions of objects with semantic structures. Lastly, we utilize an adversarial training strategy that boosts segmentation accuracy and correspondingly allows a transformer-based discriminator to capture high-level semantically correlated contents and low-level anatomical features. Our experiments demonstrate that CASTformer dramatically outperforms previous state-of-the-art transformer-based approaches on three benchmarks, obtaining 2.54%-5.88% absolute improvements in Dice over previous models. Further qualitative experiments provide a more detailed picture of the model's inner workings, shed light on the challenges in improved transparency, and demonstrate that transfer learning can greatly improve performance and reduce the size of medical image datasets in training, making CASTformer a strong starting point for downstream medical image analysis tasks.

cs.CV↗

arXiv2022

Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling

Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation laws) or from the system's design (e.g., the Jacobian matrix of a robot), even if large portions of the system dynamics remain unknown. We develop a framework to learn dynamics models from trajectory data while incorporating a-priori system knowledge as inductive bias. More specifically, the proposed framework uses physics-based side information to inform the structure of the neural network itself, and to place constraints on the values of the outputs and the internal states of the model. It represents the system's vector field as a composition of known and unknown functions, the latter of which are parametrized by neural networks. The physics-informed constraints are enforced via the augmented Lagrangian method during the model's training. We experimentally demonstrate the benefits of the proposed approach on a variety of dynamical systems -- including a benchmark suite of robotics environments featuring large state spaces, non-linear dynamics, external forces, contact forces, and control inputs. By exploiting a-priori system knowledge during training, the proposed approach learns to predict the system dynamics two orders of magnitude more accurately than a baseline approach that does not include prior knowledge, given the same training dataset.

cs.LG↗

arXiv2022

Learning Temporal Logic Properties: an Overview of Two Recent Methods

Learning linear temporal logic (LTL) formulas from examples labeled as positive or negative has found applications in inferring descriptions of system behavior. We summarize two methods to learn LTL formulas from examples in two different problem settings. The first method assumes noise in the labeling of the examples. For that, they define the problem of inferring an LTL formula that must be consistent with most but not all of the examples. The second method considers the other problem of inferring meaningful LTL formulas in the case where only positive examples are given. Hence, the first method addresses the robustness to noise, and the second method addresses the balance between conciseness and specificity (i.e., language minimality) of the inferred formula. The summarized methods propose different algorithms to solve the aforementioned problems, as well as to infer other descriptions of temporal properties, such as signal temporal logic or deterministic finite automata.

cs.LO↗

arXiv2022

Online Poisoning Attacks Against Data-Driven Predictive Control

Data-driven predictive control (DPC) is a feedback control method for systems with unknown dynamics. It repeatedly optimizes a system's future trajectories based on past input-output data. We develop a numerical method that computes poisoning attacks that inject additive perturbations to the online output data to change the trajectories optimized by DPC. This method is based on implicitly differentiating the solution map of the trajectory optimization in DPC. We demonstrate that the resulting attacks can cause an output tracking error one order of magnitude higher than random perturbations in numerical experiments.

eess.SY↗

arXiv2022

Sensor Placement for Online Fault Diagnosis

Fault diagnosis is the problem of determining a set of faulty system components that explain discrepancies between observed and expected behavior. Due to the intrinsic relation between observations and sensors placed on a system, sensors' fault diagnosis and placement are mutually dependent. Consequently, it is imperative to solve the fault diagnosis and sensor placement problems jointly. One approach to modeling systems for fault diagnosis uses answer set programming (ASP). We present a model-based approach to sensor placement for active diagnosis using ASP, where the secondary objective is to reduce the number of sensors used. The proposed method finds locations for system sensors with around 500 components in a few minutes. To address larger systems, we propose a notion of modularity such that it is possible to treat each module as a separate system and solve the sensor placement problem for each module independently. Additionally, we provide a fixpoint algorithm for determining the modules of a system.

eess.SY↗

arXiv2022

Countering Misinformation on Social Networks Using Graph Alterations

We restrict the propagation of misinformation in a social-media-like environment while preserving the spread of correct information. We model the environment as a random network of users in which each news item propagates in the network in consecutive cascades. Existing studies suggest that the cascade behaviors of misinformation and correct information are affected differently by user polarization and reflexivity. We show that this difference can be used to alter network dynamics in a way that selectively hinders the spread of misinformation content. To implement these alterations, we introduce an optimization-based probabilistic dropout method that randomly removes connections between users to achieve minimal propagation of misinformation. We use disciplined convex programming to optimize these removal probabilities over a reduced space of possible network alterations. We test the algorithm's effectiveness using simulated social networks. In our tests, we use both synthetic network structures based on stochastic block models, and natural network structures that are generated using random sampling of a dataset collected from Twitter. The results show that on average the algorithm decreases the cascade size of misinformation content by up to $70\%$ in synthetic network tests and up to $45\%$ in natural network tests while maintaining a branching ratio of at least $1.5$ for correct information.

cs.SI↗

arXiv2022

Inverse Matrix Games with Unique Quantal Response Equilibrium

In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer matrix games, where the cost perceived by each player is corrupted by random noise. We provide sufficient conditions for the players' quantal response equilibrium -- a generalization of the Nash equilibrium to games with perception noise -- to be unique. We develop efficient optimization algorithms for inferring the cost matrix based on semidefinite programs and bilevel optimization. We demonstrate the application of these methods in encouraging collision avoidance and fair resource allocation.

cs.GT↗