Mohammadhosein Hasanbeig

Mingyu Cai, Mohammadhosein Hasanbeig, Shaoping Xiao et al.

This paper investigates the motion planning of autonomous dynamical systems modeled by Markov decision processes (MDP) with unknown transition probabilities over continuous state and action spaces. Linear temporal logic (LTL) is used to specify high-level tasks over infinite horizon, which can be converted into a limit deterministic generalized Büchi automaton (LDGBA) with several accepting sets. The novelty is to design an embedded product MDP (EP-MDP) between the LDGBA and the MDP by incorporating a synchronous tracking-frontier function to record unvisited accepting sets of the automaton, and to facilitate the satisfaction of the accepting conditions. The proposed LDGBA-based reward shaping and discounting schemes for the model-free reinforcement learning (RL) only depend on the EP-MDP states and can overcome the issues of sparse rewards. Rigorous analysis shows that any RL method that optimizes the expected discounted return is guaranteed to find an optimal policy whose traces maximize the satisfaction probability. A modular deep deterministic policy gradient (DDPG) is then developed to generate such policies over continuous state and action spaces. The performance of our framework is evaluated via an array of OpenAI gym environments.

Mirco Giacobbe, Mohammadhosein Hasanbeig, Daniel Kroening et al.

Deep reinforcement learning (DRL) is applied in safety-critical domains such as robotics and autonomous driving. It achieves superhuman abilities in many tasks, however whether DRL agents can be shown to act safely is an open problem. Atari games are a simple yet challenging exemplar for evaluating the safety of DRL agents and feature a diverse portfolio of game mechanics. The safety of neural agents has been studied before using methods that either require a model of the system dynamics or an abstraction; unfortunately, these are unsuitable to Atari games because their low-level dynamics are complex and hidden inside their emulator. We present the first exact method for analysing and ensuring the safety of DRL agents for Atari games. Our method only requires access to the emulator. First, we give a set of 43 properties that characterise "safe behaviour" for 30 games. Second, we develop a method for exploring all traces induced by an agent and a game and consider a variety of sources of game non-determinism. We observe that the best available DRL agents reliably satisfy only very few properties; several critical properties are violated by all agents. Finally, we propose a countermeasure that combines a bounded explicit-state exploration with shielding. We demonstrate that our method improves the safety of all agents over multiple properties.

Thomas J. Ringstrom, Mohammadhosein Hasanbeig, Alessandro Abate

In the domain of hierarchical planning, compositionality, abstraction, and task transfer are crucial for designing algorithms that can efficiently solve a variety of problems with maximal representational reuse. Many real-world problems require non-Markovian policies to handle complex structured tasks with logical conditions, often leading to prohibitively large state representations; this requires efficient methods for breaking these problems down and reusing structure between tasks. To this end, we introduce a compositional framework called Linearly-Solvable Goal Kernel Dynamic Programming (LS-GKDP) to address the complexity of solving non-Markovian Boolean sub-goal tasks with ordering constraints. LS-GKDP combines the Linearly-Solvable Markov Decision Process (LMDP) formalism with the Options Framework of Reinforcement Learning. LMDPs can be efficiently solved as a principal eigenvector problem, and options are policies with termination conditions used as temporally extended actions; with LS-GKDP we expand LMDPs to control over options for logical tasks. This involves decomposing a high-dimensional problem down into a set of goal-condition options for each goal and constructing a goal kernel, which is an abstract transition kernel that jumps from an option's initial-states to its termination-states along with an update of the higher-level task-state. We show how an LMDP with a goal kernel enables the efficient optimization of meta-policies in a lower-dimensional subspace defined by the task grounding. Options can also be remapped to new problems within a super-exponential space of tasks without significant recomputation, and we identify cases where the solution is invariant to the task grounding, permitting zero-shot task transfer.

Mohammadhosein Hasanbeig, Alessandro Abate, Daniel Kroening

This paper presents the concept of an adaptive safe padding that forces Reinforcement Learning (RL) to synthesise optimal control policies while ensuring safety during the learning process. Policies are synthesised to satisfy a goal, expressed as a temporal logic formula, with maximal probability. Enforcing the RL agent to stay safe during learning might limit the exploration, however we show that the proposed architecture is able to automatically handle the trade-off between efficient progress in exploration (towards goal satisfaction) and ensuring safety. Theoretical guarantees are available on the optimality of the synthesised policies and on the convergence of the learning algorithm. Experimental results are provided to showcase the performance of the proposed method.

Mohammadhosein Hasanbeig, Natasha Yogananda Jeppu, Alessandro Abate et al.

This paper proposes DeepSynth, a method for effective training of deep Reinforcement Learning (RL) agents when the reward is sparse and non-Markovian, but at the same time progress towards the reward requires achieving an unknown sequence of high-level objectives. Our method employs a novel algorithm for synthesis of compact automata to uncover this sequential structure automatically. We synthesise a human-interpretable automaton from trace data collected by exploring the environment. The state space of the environment is then enriched with the synthesised automaton so that the generation of a control policy by deep RL is guided by the discovered structure encoded in the automaton. The proposed approach is able to cope with both high-dimensional, low-level features and unknown sparse non-Markovian rewards. We have evaluated DeepSynth's performance in a set of experiments that includes the Atari game Montezuma's Revenge. Compared to existing approaches, we obtain a reduction of two orders of magnitude in the number of iterations required for policy synthesis, and also a significant improvement in scalability.

Lim Zun Yuan, Mohammadhosein Hasanbeig, Alessandro Abate et al.

We propose an actor-critic, model-free, and online Reinforcement Learning (RL) framework for continuous-state continuous-action Markov Decision Processes (MDPs) when the reward is highly sparse but encompasses a high-level temporal structure. We represent this temporal structure by a finite-state machine and construct an on-the-fly synchronised product with the MDP and the finite machine. The temporal structure acts as a guide for the RL agent within the product, where a modular Deep Deterministic Policy Gradient (DDPG) architecture is proposed to generate a low-level control policy. We evaluate our framework in a Mars rover experiment and we present the success rate of the synthesised policy.

Mohammadhosein Hasanbeig, Yiannis Kantaros, Alessandro Abate et al.

Reinforcement Learning (RL) has emerged as an efficient method of choice for solving complex sequential decision making problems in automatic control, computer science, economics, and biology. In this paper we present a model-free RL algorithm to synthesize control policies that maximize the probability of satisfying high-level control objectives given as Linear Temporal Logic (LTL) formulas. Uncertainty is considered in the workspace properties, the structure of the workspace, and the agent actions, giving rise to a Probabilistically-Labeled Markov Decision Process (PL-MDP) with unknown graph structure and stochastic behaviour, which is even more general case than a fully unknown MDP. We first translate the LTL specification into a Limit Deterministic Buchi Automaton (LDBA), which is then used in an on-the-fly product with the PL-MDP. Thereafter, we define a synchronous reward function based on the acceptance condition of the LDBA. Finally, we show that the RL algorithm delivers a policy that maximizes the satisfaction probability asymptotically. We provide experimental results that showcase the efficiency of the proposed method.

Mohammadhosein Hasanbeig, Alessandro Abate, Daniel Kroening

We propose a method for efficient training of Q-functions for continuous-state Markov Decision Processes (MDPs) such that the traces of the resulting policies satisfy a given Linear Temporal Logic (LTL) property. LTL, a modal logic, can express a wide range of time-dependent logical properties (including "safety") that are quite similar to patterns in natural language. We convert the LTL property into a limit deterministic Buchi automaton and construct an on-the-fly synchronised product MDP. The control policy is then synthesised by defining an adaptive reward function and by applying a modified neural fitted Q-iteration algorithm to the synchronised structure, assuming that no prior knowledge is available from the original MDP. The proposed method is evaluated in a numerical study to test the quality of the generated control policy and is compared with conventional methods for policy synthesis such as MDP abstraction (Voronoi quantizer) and approximate dynamic programming (fitted value iteration).

Mohammadhosein Hasanbeig, Lacra Pavel

The main focus of this paper is on enhancement of two types of game-theoretic learning algorithms: log-linear learning and reinforcement learning. The standard analysis of log-linear learning needs a highly structured environment, i.e. strong assumptions about the game from an implementation perspective. In this paper, we introduce a variant of log-linear learning that provides asymptotic guarantees while relaxing the structural assumptions to include synchronous updates and limitations in information available to the players. On the other hand, model-free reinforcement learning is able to perform even under weaker assumptions on players' knowledge about the environment and other players' strategies. We propose a reinforcement algorithm that uses a double-aggregation scheme in order to deepen players' insight about the environment and constant learning step-size which achieves a higher convergence rate. Numerical experiments are conducted to verify each algorithm's robustness and performance.

Mohammadhosein Hasanbeig, Alessandro Abate, Daniel Kroening

We present the first model-free Reinforcement Learning (RL) algorithm to synthesise policies for an unknown Markov Decision Process (MDP), such that a linear time property is satisfied. The given temporal property is converted into a Limit Deterministic Buchi Automaton (LDBA) and a robust reward function is defined over the state-action pairs of the MDP according to the resulting LDBA. With this reward function, the policy synthesis procedure is "constrained" by the given specification. These constraints guide the MDP exploration so as to minimize the solution time by only considering the portion of the MDP that is relevant to satisfaction of the LTL property. This improves performance and scalability of the proposed method by avoiding an exhaustive update over the whole state space while the efficiency of standard methods such as dynamic programming is hindered by excessive memory requirements, caused by the need to store a full-model in memory. Additionally, we show that the RL procedure sets up a local value iteration method to efficiently calculate the maximum probability of satisfying the given property, at any given state of the MDP. We prove that our algorithm is guaranteed to find a policy whose traces probabilistically satisfy the LTL property if such a policy exists, and additionally we show that our method produces reasonable control policies even when the LTL property cannot be satisfied. The performance of the algorithm is evaluated via a set of numerical examples. We observe an improvement of one order of magnitude in the number of iterations required for the synthesis compared to existing approaches.