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Multi-Agent Reinforcement Learning with Temporal Logic Specifications2021-01-31   ${\displaystyle \cong }$
In this paper, we study the problem of learning to satisfy temporal logic specifications with a group of agents in an unknown environment, which may exhibit probabilistic behaviour. From a learning perspective these specifications provide a rich formal language with which to capture tasks or objectives, while from a logic and automated verification perspective the introduction of learning capabilities allows for practical applications in large, stochastic, unknown environments. The existing work in this area is, however, limited. Of the frameworks that consider full linear temporal logic or have correctness guarantees, all methods thus far consider only the case of a single temporal logic specification and a single agent. In order to overcome this limitation, we develop the first multi-agent reinforcement learning technique for temporal logic specifications, which is also novel in its ability to handle multiple specifications. We provide correctness and convergence guarantees for our main algorithm - ALMANAC (Automaton/Logic Multi-Agent Natural Actor-Critic) - even when using function approximation. Alongside our theoretical results, we further demonstrate the applicability of our technique via a set of preliminary experiments.
Feature Interactions on Steroids: On the Composition of ML Models2021-05-13   ${\displaystyle \cong }$
The lack of specifications is a key difference between traditional software engineering and machine learning. We discuss how it drastically impacts how we think about divide-and-conquer approaches to system design, and how it impacts reuse, testing and debugging activities. Traditionally, specifications provide a cornerstone for compositional reasoning and for the divide-and-conquer strategy of how we build large and complex systems from components, but those are hard to come by for machine-learned components. While the lack of specification seems like a fundamental new problem at first sight, in fact software engineers routinely deal with iffy specifications in practice: we face weak specifications, wrong specifications, and unanticipated interactions among components and their specifications. Machine learning may push us further, but the problems are not fundamentally new. Rethinking machine-learning model composition from the perspective of the feature interaction problem, we may even teach us a thing or two on how to move forward, including the importance of integration testing, of requirements engineering, and of design.
Inverse Reinforcement Learning of Autonomous Behaviors Encoded as Weighted Finite Automata2021-03-10   ${\displaystyle \cong }$
This paper presents a method for learning logical task specifications and cost functions from demonstrations. Linear temporal logic (LTL) formulas are widely used to express complex objectives and constraints for autonomous systems. Yet, such specifications may be challenging to construct by hand. Instead, we consider demonstrated task executions, whose temporal logic structure and transition costs need to be inferred by an autonomous agent. We employ a spectral learning approach to extract a weighted finite automaton (WFA), approximating the unknown logic structure of the task. Thereafter, we define a product between the WFA for high-level task guidance and a Labeled Markov decision process (L-MDP) for low-level control and optimize a cost function that matches the demonstrator's behavior. We demonstrate that our method is capable of generalizing the execution of the inferred task specification to new environment configurations.
Correct-by-synthesis reinforcement learning with temporal logic constraints2015-03-05   ${\displaystyle \cong }$
We consider a problem on the synthesis of reactive controllers that optimize some a priori unknown performance criterion while interacting with an uncontrolled environment such that the system satisfies a given temporal logic specification. We decouple the problem into two subproblems. First, we extract a (maximally) permissive strategy for the system, which encodes multiple (possibly all) ways in which the system can react to the adversarial environment and satisfy the specifications. Then, we quantify the a priori unknown performance criterion as a (still unknown) reward function and compute an optimal strategy for the system within the operating envelope allowed by the permissive strategy by using the so-called maximin-Q learning algorithm. We establish both correctness (with respect to the temporal logic specifications) and optimality (with respect to the a priori unknown performance criterion) of this two-step technique for a fragment of temporal logic specifications. For specifications beyond this fragment, correctness can still be preserved, but the learned strategy may be sub-optimal. We present an algorithm to the overall problem, and demonstrate its use and computational requirements on a set of robot motion planning examples.
Elaborating on Learned Demonstrations with Temporal Logic Specifications2020-05-22   ${\displaystyle \cong }$
Most current methods for learning from demonstrations assume that those demonstrations alone are sufficient to learn the underlying task. This is often untrue, especially if extra safety specifications exist which were not present in the original demonstrations. In this paper, we allow an expert to elaborate on their original demonstration with additional specification information using linear temporal logic (LTL). Our system converts LTL specifications into a differentiable loss. This loss is then used to learn a dynamic movement primitive that satisfies the underlying specification, while remaining close to the original demonstration. Further, by leveraging adversarial training, our system learns to robustly satisfy the given LTL specification on unseen inputs, not just those seen in training. We show that our method is expressive enough to work across a variety of common movement specification patterns such as obstacle avoidance, patrolling, keeping steady, and speed limitation. In addition, we show that our system can modify a base demonstration with complex specifications by incrementally composing multiple simpler specifications. We also implement our system on a PR-2 robot to show how a demonstrator can start with an initial (sub-optimal) demonstration, then interactively improve task success by including additional specifications enforced with our differentiable LTL loss.
Using Logical Specifications of Objectives in Multi-Objective Reinforcement Learning2020-05-06   ${\displaystyle \cong }$
In the multi-objective reinforcement learning (MORL) paradigm, the relative importance of each environment objective is often unknown prior to training, so agents must learn to specialize their behavior to optimize different combinations of environment objectives that are specified post-training. These are typically linear combinations, so the agent is effectively parameterized by a weight vector that describes how to balance competing environment objectives. However, many real world behaviors require non-linear combinations of objectives. Additionally, the conversion between desired behavior and weightings is often unclear. In this work, we explore the use of a language based on propositional logic with quantitative semantics--in place of weight vectors--for specifying non-linear behaviors in an interpretable way. We use a recurrent encoder to encode logical combinations of objectives, and train a MORL agent to generalize over these encodings. We test our agent in several environments with various objectives and show that our agent can generalize to many never-before-seen specifications with performance comparable to single policy baseline agents. We also demonstrate our agent's ability to generate meaningful policies when presented with novel specifications and quickly specialize to novel specifications.
Learning Task Specifications from Demonstrations2018-10-27   ${\displaystyle \cong }$
Real world applications often naturally decompose into several sub-tasks. In many settings (e.g., robotics) demonstrations provide a natural way to specify the sub-tasks. However, most methods for learning from demonstrations either do not provide guarantees that the artifacts learned for the sub-tasks can be safely recombined or limit the types of composition available. Motivated by this deficit, we consider the problem of inferring Boolean non-Markovian rewards (also known as logical trace properties or specifications) from demonstrations provided by an agent operating in an uncertain, stochastic environment. Crucially, specifications admit well-defined composition rules that are typically easy to interpret. In this paper, we formulate the specification inference task as a maximum a posteriori (MAP) probability inference problem, apply the principle of maximum entropy to derive an analytic demonstration likelihood model and give an efficient approach to search for the most likely specification in a large candidate pool of specifications. In our experiments, we demonstrate how learning specifications can help avoid common problems that often arise due to ad-hoc reward composition.
Statistically Model Checking PCTL Specifications on Markov Decision Processes via Reinforcement Learning2020-04-21   ${\displaystyle \cong }$
Probabilistic Computation Tree Logic (PCTL) is frequently used to formally specify control objectives such as probabilistic reachability and safety. In this work, we focus on model checking PCTL specifications statistically on Markov Decision Processes (MDPs) by sampling, e.g., checking whether there exists a feasible policy such that the probability of reaching certain goal states is greater than a threshold. We use reinforcement learning to search for such a feasible policy for PCTL specifications, and then develop a statistical model checking (SMC) method with provable guarantees on its error. Specifically, we first use upper-confidence-bound (UCB) based Q-learning to design an SMC algorithm for bounded-time PCTL specifications, and then extend this algorithm to unbounded-time specifications by identifying a proper truncation time by checking the PCTL specification and its negation at the same time. Finally, we evaluate the proposed method on case studies.
Foundations for Restraining Bolts: Reinforcement Learning with LTLf/LDLf restraining specifications2019-11-11   ${\displaystyle \cong }$
In this work we investigate on the concept of "restraining bolt", envisioned in Science Fiction. Specifically we introduce a novel problem in AI. We have two distinct sets of features extracted from the world, one by the agent and one by the authority imposing restraining specifications (the "restraining bolt"). The two sets are apparently unrelated since of interest to independent parties, however they both account for (aspects of) the same world. We consider the case in which the agent is a reinforcement learning agent on the first set of features, while the restraining bolt is specified logically using linear time logic on finite traces LTLf/LDLf over the second set of features. We show formally, and illustrate with examples, that, under general circumstances, the agent can learn while shaping its goals to suitably conform (as much as possible) to the restraining bolt specifications.
CounterExample Guided Neural Synthesis2020-01-24   ${\displaystyle \cong }$
Program synthesis is the generation of a program from a specification. Correct synthesis is difficult, and methods that provide formal guarantees suffer from scalability issues. On the other hand, neural networks are able to generate programs from examples quickly but are unable to guarantee that the program they output actually meets the logical specification. In this work we combine neural networks with formal reasoning: using the latter to convert a logical specification into a sequence of examples that guides the neural network towards a correct solution, and to guarantee that any solution returned satisfies the formal specification. We apply our technique to synthesising loop invariants and compare the performance to existing solvers that use SMT and existing techniques that use neural networks. Our results show that the formal reasoning based guidance improves the performance of the neural network substantially, nearly doubling the number of benchmarks it can solve.
Tractable Reinforcement Learning of Signal Temporal Logic Objectives2020-02-17   ${\displaystyle \cong }$
Signal temporal logic (STL) is an expressive language to specify time-bound real-world robotic tasks and safety specifications. Recently, there has been an interest in learning optimal policies to satisfy STL specifications via reinforcement learning (RL). Learning to satisfy STL specifications often needs a sufficient length of state history to compute reward and the next action. The need for history results in exponential state-space growth for the learning problem. Thus the learning problem becomes computationally intractable for most real-world applications. In this paper, we propose a compact means to capture state history in a new augmented state-space representation. An approximation to the objective (maximizing probability of satisfaction) is proposed and solved for in the new augmented state-space. We show the performance bound of the approximate solution and compare it with the solution of an existing technique via simulations.
Synthesizing Skeletons for Reactive Systems2018-03-25   ${\displaystyle \cong }$
We present an analysis technique for temporal specifications of reactive systems that identifies, on the level of individual system outputs over time, which parts of the implementation are determined by the specification, and which parts are still open. This information is represented in the form of a labeled transition system, which we call skeleton. Each state of the skeleton is labeled with a three-valued assignment to the output variables: each output can be true, false, or open, where true or false means that the value must be true or false, respectively, and open means that either value is still possible. We present algorithms for the verification of skeletons and for the learning-based synthesis of skeletons from specifications in linear-time temporal logic (LTL). The algorithm returns a skeleton that satisfies the given LTL specification in time polynomial in the size of the minimal skeleton. Our new analysis technique can be used to recognize and repair specifications that underspecify critical situations. The technique thus complements existing methods for the recognition and repair of overspecifications via the identification of unrealizable cores.
Neural Task Programming: Learning to Generalize Across Hierarchical Tasks2018-03-14   ${\displaystyle \cong }$
In this work, we propose a novel robot learning framework called Neural Task Programming (NTP), which bridges the idea of few-shot learning from demonstration and neural program induction. NTP takes as input a task specification (e.g., video demonstration of a task) and recursively decomposes it into finer sub-task specifications. These specifications are fed to a hierarchical neural program, where bottom-level programs are callable subroutines that interact with the environment. We validate our method in three robot manipulation tasks. NTP achieves strong generalization across sequential tasks that exhibit hierarchal and compositional structures. The experimental results show that NTP learns to generalize well to- wards unseen tasks with increasing lengths, variable topologies, and changing objectives.
Verifying Probabilistic Specifications with Functional Lagrangians2021-02-18   ${\displaystyle \cong }$
We propose a general framework for verifying input-output specifications of neural networks using functional Lagrange multipliers that generalizes standard Lagrangian duality. We derive theoretical properties of the framework, which can handle arbitrary probabilistic specifications, showing that it provably leads to tight verification when a sufficiently flexible class of functional multipliers is chosen. With a judicious choice of the class of functional multipliers, the framework can accommodate desired trade-offs between tightness and complexity. We demonstrate empirically that the framework can handle a diverse set of networks, including Bayesian neural networks with Gaussian posterior approximations, MC-dropout networks, and verify specifications on adversarial robustness and out-of-distribution(OOD) detection. Our framework improves upon prior work in some settings and also generalizes to new stochastic networks and probabilistic specifications, like distributionally robust OOD detection.
A New SVDD-Based Multivariate Non-parametric Process Capability Index2018-11-13   ${\displaystyle \cong }$
Process capability index (PCI) is a commonly used statistic to measure ability of a process to operate within the given specifications or to produce products which meet the required quality specifications. PCI can be univariate or multivariate depending upon the number of process specifications or quality characteristics of interest. Most PCIs make distributional assumptions which are often unrealistic in practice. This paper proposes a new multivariate non-parametric process capability index. This index can be used when distribution of the process or quality parameters is either unknown or does not follow commonly used distributions such as multivariate normal.
Three Modern Roles for Logic in AI2020-04-18   ${\displaystyle \cong }$
We consider three modern roles for logic in artificial intelligence, which are based on the theory of tractable Boolean circuits: (1) logic as a basis for computation, (2) logic for learning from a combination of data and knowledge, and (3) logic for reasoning about the behavior of machine learning systems.
Enabling Open-World Specification Mining via Unsupervised Learning2019-04-26   ${\displaystyle \cong }$
Many programming tasks require using both domain-specific code and well-established patterns (such as routines concerned with file IO). Together, several small patterns combine to create complex interactions. This compounding effect, mixed with domain-specific idiosyncrasies, creates a challenging environment for fully automatic specification inference. Mining specifications in this environment, without the aid of rule templates, user-directed feedback, or predefined API surfaces, is a major challenge. We call this challenge Open-World Specification Mining. In this paper, we present a framework for mining specifications and usage patterns in an Open-World setting. We design this framework to be miner-agnostic and instead focus on disentangling complex and noisy API interactions. To evaluate our framework, we introduce a benchmark of 71 clusters extracted from five open-source projects. Using this dataset, we show that interesting clusters can be recovered, in a fully automatic way, by leveraging unsupervised learning in the form of word embeddings. Once clusters have been recovered, the challenge of Open-World Specification Mining is simplified and any trace-based mining technique can be applied. In addition, we provide a comprehensive evaluation of three word-vector learners to showcase the value of sub-word information for embeddings learned in the software-engineering domain.
Verifiable Planning in Expected Reward Multichain MDPs2020-12-03   ${\displaystyle \cong }$
The planning domain has experienced increased interest in the formal synthesis of decision-making policies. This formal synthesis typically entails finding a policy which satisfies formal specifications in the form of some well-defined logic, such as Linear Temporal Logic (LTL) or Computation Tree Logic (CTL), among others. While such logics are very powerful and expressive in their capacity to capture desirable agent behavior, their value is limited when deriving decision-making policies which satisfy certain types of asymptotic behavior. In particular, we are interested in specifying constraints on the steady-state behavior of an agent, which captures the proportion of time an agent spends in each state as it interacts for an indefinite period of time with its environment. This is sometimes called the average or expected behavior of the agent. In this paper, we explore the steady-state planning problem of deriving a decision-making policy for an agent such that constraints on its steady-state behavior are satisfied. A linear programming solution for the general case of multichain Markov Decision Processes (MDPs) is proposed and we prove that optimal solutions to the proposed programs yield stationary policies with rigorous guarantees of behavior.
Probably Approximately Correct MDP Learning and Control With Temporal Logic Constraints2014-04-30   ${\displaystyle \cong }$
We consider synthesis of control policies that maximize the probability of satisfying given temporal logic specifications in unknown, stochastic environments. We model the interaction between the system and its environment as a Markov decision process (MDP) with initially unknown transition probabilities. The solution we develop builds on the so-called model-based probably approximately correct Markov decision process (PAC-MDP) methodology. The algorithm attains an $\varepsilon$-approximately optimal policy with probability $1-?$ using samples (i.e. observations), time and space that grow polynomially with the size of the MDP, the size of the automaton expressing the temporal logic specification, $\frac{1}{\varepsilon}$, $\frac{1}?$ and a finite time horizon. In this approach, the system maintains a model of the initially unknown MDP, and constructs a product MDP based on its learned model and the specification automaton that expresses the temporal logic constraints. During execution, the policy is iteratively updated using observation of the transitions taken by the system. The iteration terminates in finitely many steps. With high probability, the resulting policy is such that, for any state, the difference between the probability of satisfying the specification under this policy and the optimal one is within a predefined bound.
Learning from Demonstrations using Signal Temporal Logic2021-02-15   ${\displaystyle \cong }$
Learning-from-demonstrations is an emerging paradigm to obtain effective robot control policies for complex tasks via reinforcement learning without the need to explicitly design reward functions. However, it is susceptible to imperfections in demonstrations and also raises concerns of safety and interpretability in the learned control policies. To address these issues, we use Signal Temporal Logic to evaluate and rank the quality of demonstrations. Temporal logic-based specifications allow us to create non-Markovian rewards, and also define interesting causal dependencies between tasks such as sequential task specifications. We validate our approach through experiments on discrete-world and OpenAI Gym environments, and show that our approach outperforms the state-of-the-art Maximum Causal Entropy Inverse Reinforcement Learning.