Error Analysis of Band Matrix Method

Numerical error in the solution of the band matrix method based on the elimination method in single precision is investigated theoretically and experimentally, and the behaviour of the truncation error and the roundoff error is clarified. Some important suggestions for the useful application of the band solver are proposed by using the results of above error analysis

Control as Probabilistic Inference as an Emergent Communication Mechanism in Multi-Agent Reinforcement Learning

This paper proposes a generative probabilistic model integrating emergent communication and multi-agent reinforcement learning. The agents plan their actions by probabilistic inference, called control as inference, and communicate using messages that are latent variables and estimated based on the planned actions. Through these messages, each agent can send information about its actions and know information about the actions of another agent. Therefore, the agents change their actions according to the estimated messages to achieve cooperative tasks. This inference of messages can be considered as communication, and this procedure can be formulated by the Metropolis-Hasting naming game. Through experiments in the grid world environment, we show that the proposed PGM can infer meaningful messages to achieve the cooperative task

Integration of Imitation Learning using GAIL and Reinforcement Learning using Task-achievement Rewards via Probabilistic Graphical Model

Integration of reinforcement learning and imitation learning is an important problem that has been studied for a long time in the field of intelligent robotics. Reinforcement learning optimizes policies to maximize the cumulative reward, whereas imitation learning attempts to extract general knowledge about the trajectories demonstrated by experts, i.e., demonstrators. Because each of them has their own drawbacks, methods combining them and compensating for each set of drawbacks have been explored thus far. However, many of the methods are heuristic and do not have a solid theoretical basis. In this paper, we present a new theory for integrating reinforcement and imitation learning by extending the probabilistic generative model framework for reinforcement learning, {\it plan by inference}. We develop a new probabilistic graphical model for reinforcement learning with multiple types of rewards and a probabilistic graphical model for Markov decision processes with multiple optimality emissions (pMDP-MO). Furthermore, we demonstrate that the integrated learning method of reinforcement learning and imitation learning can be formulated as a probabilistic inference of policies on pMDP-MO by considering the output of the discriminator in generative adversarial imitation learning as an additional optimal emission observation. We adapt the generative adversarial imitation learning and task-achievement reward to our proposed framework, achieving significantly better performance than agents trained with reinforcement learning or imitation learning alone. Experiments demonstrate that our framework successfully integrates imitation and reinforcement learning even when the number of demonstrators is only a few.Comment: Submitted to Advanced Robotic

Symbol emergence as interpersonal cross-situational learning: the emergence of lexical knowledge with combinatoriality

We present a computational model for a symbol emergence system that enables the emergence of lexical knowledge with combinatoriality among agents through a Metropolis-Hastings naming game and cross-situational learning. Many computational models have been proposed to investigate combinatoriality in emergent communication and symbol emergence in cognitive and developmental robotics. However, existing models do not sufficiently address category formation based on sensory-motor information and semiotic communication through the exchange of word sequences within a single integrated model. Our proposed model facilitates the emergence of lexical knowledge with combinatoriality by performing category formation using multimodal sensory-motor information and enabling semiotic communication through the exchange of word sequences among agents in a unified model. Furthermore, the model enables an agent to predict sensory-motor information for unobserved situations by combining words associated with categories in each modality. We conducted two experiments with two humanoid robots in a simulated environment to evaluate our proposed model. The results demonstrated that the agents can acquire lexical knowledge with combinatoriality through interpersonal cross-situational learning based on the Metropolis-Hastings naming game and cross-situational learning. Furthermore, our results indicate that the lexical knowledge developed using our proposed model exhibits generalization performance for novel situations through interpersonal cross-modal inference