Kenji Doya

Florian Lalande, Kenji Doya

Numerical data imputation algorithms replace missing values by estimates to leverage incomplete data sets. Current imputation methods seek to minimize the error between the unobserved ground truth and the imputed values. But this strategy can create artifacts leading to poor imputation in the presence of multimodal or complex distributions. To tackle this problem, we introduce the $k$NN$\times$KDE algorithm: a data imputation method combining nearest neighbor estimation ($k$NN) and density estimation with Gaussian kernels (KDE). We compare our method with previous data imputation methods using artificial and real-world data with different data missing scenarios and various data missing rates, and show that our method can cope with complex original data structure, yields lower data imputation errors, and provides probabilistic estimates with higher likelihood than current methods. We release the code in open-source for the community: https://github.com/DeltaFloflo/knnxkde

Dongqi Han, Kenji Doya, Dongsheng Li et al.

How to behave efficiently and flexibly is a central problem for understanding biological agents and creating intelligent embodied AI. It has been well known that behavior can be classified as two types: reward-maximizing habitual behavior, which is fast while inflexible; and goal-directed behavior, which is flexible while slow. Conventionally, habitual and goal-directed behaviors are considered handled by two distinct systems in the brain. Here, we propose to bridge the gap between the two behaviors, drawing on the principles of variational Bayesian theory. We incorporate both behaviors in one framework by introducing a Bayesian latent variable called "intention". The habitual behavior is generated by using prior distribution of intention, which is goal-less; and the goal-directed behavior is generated by the posterior distribution of intention, which is conditioned on the goal. Building on this idea, we present a novel Bayesian framework for modeling behaviors. Our proposed framework enables skill sharing between the two kinds of behaviors, and by leveraging the idea of predictive coding, it enables an agent to seamlessly generalize from habitual to goal-directed behavior without requiring additional training. The proposed framework suggests a fresh perspective for cognitive science and embodied AI, highlighting the potential for greater integration between habitual and goal-directed behaviors.

Sutashu Tomonaga, Kenji Doya, Noboru Murata

Structured State Space Models (SSMs), which are at the heart of the recently popular Mamba architecture, are powerful tools for sequence modeling. However, their theoretical foundation relies on a complex, multi-stage process of continuous-time modeling and subsequent discretization, which can obscure intuition. We introduce a direct, first-principles framework for constructing discrete-time SSMs that is both flexible and modular. Our approach is based on a novel lag operator, which geometrically derives the discrete-time recurrence by measuring how the system's basis functions "slide" and change from one timestep to the next. The resulting state matrices are computed via a single inner product involving this operator, offering a modular design space for creating novel SSMs by flexibly combining different basis functions and time-warping schemes. To validate our approach, we demonstrate that a specific instance exactly recovers the recurrence of the influential HiPPO model. Numerical simulations confirm our derivation, providing new theoretical tools for designing flexible and robust sequence models.

Theodore Jerome Tinker, Kenji Doya, Jun Tani

In Reinforcement Learning (RL), artificial agents are trained to maximize numerical rewards by performing tasks. Exploration is essential in RL because agents must discover information before exploiting it. Two rewards encouraging efficient exploration are the entropy of action policy and curiosity for information gain. Entropy is well-established in literature, promoting randomized action selection. Curiosity is defined in a broad variety of ways in literature, promoting discovery of novel experiences. One example, prediction error curiosity, rewards agents for discovering observations they cannot accurately predict. However, such agents may be distracted by unpredictable observational noises known as curiosity traps. Based on the Free Energy Principle (FEP), this paper proposes hidden state curiosity, which rewards agents by the KL divergence between the predictive prior and posterior probabilities of latent variables. We trained six types of agents to navigate mazes: baseline agents without rewards for entropy or curiosity, and agents rewarded for entropy and/or either prediction error curiosity or hidden state curiosity. We find entropy and curiosity result in efficient exploration, especially both employed together. Notably, agents with hidden state curiosity demonstrate resilience against curiosity traps, which hinder agents with prediction error curiosity. This suggests implementing the FEP may enhance the robustness and generalization of RL models, potentially aligning the learning processes of artificial and biological agents.

Theodore Jerome Tinker, Kenji Doya, Jun Tani

Human infants acquire language and action gradually through development, achieving remarkable generalization capabilities from only a minimal number of learning examples. In contrast, recent large language models require exposure to billions of training tokens to achieve such generalization. What mechanisms underlie such efficient developmental learning in humans? This study addresses this question through simulation experiments in which robots learn to perform various actions corresponding to imperative sentences (e.g., \textit{push red cube}) via trials of self-guided exploration. Our approach integrates the active inference framework with reinforcement learning, enabling curiosity-driven developmental learning. The simulations yielded several important findings: i) Generalization is drastically improved as the number of compositional elements increases. ii) Curiosity-driven exploration combined with motor noise substantially outperforms learning without curiosity. iii) Rote pairing of sentences and actions occurs before the emergence of compositional generalization. iv) Simpler, prerequisite-like actions emerge earlier in development, while more complex actions involving these prerequisites develop later. These results shed light into possible mechanisms underlying efficient developmental learning in infants and provide computational parallels to findings in developmental psychology.

Yuji Kanagawa, Kenji Doya

Fear is a critical brain function for detecting danger and learning to avoid specific stimuli that can lead to danger. While fear is believed to have evolved under pressure from predators, experimentally reproducing the evolution is challenging. To investigate the relationship between environmental conditions, the evolution of fear, and the evolution of other rewards, such as food reward and social reward, we developed a distributed evolutionary simulation. In our simulation, prey and predator agents co-evolve their innate reward functions, including a possibly fear-like term for observing predators, and learn behaviors via reinforcement learning. Surprisingly, our simulation revealed that social reward for observing the same species is more important for prey to survive, and fear-like negative reward for observing predators evolves only after acquiring social reward. We also found that the predator with increased hunting ability (larger mouth) amplified fear emergence, but also that fear evolution is more stable with non-evolving predators that are bad at chasing prey. Additionally, unlike for predators, we found that positive rewards evolve in opposition to fear for stationary threats, as areas with abundant leftover food develop around them. These findings suggest that fear and social reward have had a complex interplay with each other through evolution, along with the nature of predators and threats.

Yuji Kanagawa, Kenji Doya

The reward system is one of the fundamental drivers of animal behaviors and is critical for survival and reproduction. Despite its importance, the problem of how the reward system has evolved is underexplored. In this paper, we try to replicate the evolution of biologically plausible reward functions and investigate how environmental conditions affect evolved rewards' shape. For this purpose, we developed a population-based decentralized evolutionary simulation framework, where agents maintain their energy level to live longer and produce more children. Each agent inherits its reward function from its parent subject to mutation and learns to get rewards via reinforcement learning throughout its lifetime. Our results show that biologically reasonable positive rewards for food acquisition and negative rewards for motor action can evolve from randomly initialized ones. However, we also find that the rewards for motor action diverge into two modes: largely positive and slightly negative. The emergence of positive motor action rewards is surprising because it can make agents too active and inefficient in foraging. In environments with poor and poisonous foods, the evolution of rewards for less important foods tends to be unstable, while rewards for normal foods are still stable. These results demonstrate the usefulness of our simulation environment and energy-dependent birth and death model for further studies of the origin of reward systems.

Dongqi Han, Kenji Doya, Jun Tani

What is the difference between goal-directed and habitual behavior? We propose a novel computational framework of decision making with Bayesian inference, in which everything is integrated as an entire neural network model. The model learns to predict environmental state transitions by self-exploration and generating motor actions by sampling stochastic internal states ${z}$. Habitual behavior, which is obtained from the prior distribution of ${z}$, is acquired by reinforcement learning. Goal-directed behavior is determined from the posterior distribution of ${z}$ by planning, using active inference which optimizes the past, current and future ${z}$ by minimizing the variational free energy for the desired future observation constrained by the observed sensory sequence. We demonstrate the effectiveness of the proposed framework by experiments in a sensorimotor navigation task with camera observations and continuous motor actions.

Tadahiro Taniguchi, Hiroshi Yamakawa, Takayuki Nagai et al.

Building a humanlike integrative artificial cognitive system, that is, an artificial general intelligence (AGI), is the holy grail of the artificial intelligence (AI) field. Furthermore, a computational model that enables an artificial system to achieve cognitive development will be an excellent reference for brain and cognitive science. This paper describes an approach to develop a cognitive architecture by integrating elemental cognitive modules to enable the training of the modules as a whole. This approach is based on two ideas: (1) brain-inspired AI, learning human brain architecture to build human-level intelligence, and (2) a probabilistic generative model(PGM)-based cognitive system to develop a cognitive system for developmental robots by integrating PGMs. The development framework is called a whole brain PGM (WB-PGM), which differs fundamentally from existing cognitive architectures in that it can learn continuously through a system based on sensory-motor information. In this study, we describe the rationale of WB-PGM, the current status of PGM-based elemental cognitive modules, their relationship with the human brain, the approach to the integration of the cognitive modules, and future challenges. Our findings can serve as a reference for brain studies. As PGMs describe explicit informational relationships between variables, this description provides interpretable guidance from computational sciences to brain science. By providing such information, researchers in neuroscience can provide feedback to researchers in AI and robotics on what the current models lack with reference to the brain. Further, it can facilitate collaboration among researchers in neuro-cognitive sciences as well as AI and robotics.

Eiji Uchibe, Kenji Doya

This paper proposes model-free imitation learning named Entropy-Regularized Imitation Learning (ERIL) that minimizes the reverse Kullback-Leibler (KL) divergence. ERIL combines forward and inverse reinforcement learning (RL) under the framework of an entropy-regularized Markov decision process. An inverse RL step computes the log-ratio between two distributions by evaluating two binary discriminators. The first discriminator distinguishes the state generated by the forward RL step from the expert's state. The second discriminator, which is structured by the theory of entropy regularization, distinguishes the state-action-next-state tuples generated by the learner from the expert ones. One notable feature is that the second discriminator shares hyperparameters with the forward RL, which can be used to control the discriminator's ability. A forward RL step minimizes the reverse KL estimated by the inverse RL step. We show that minimizing the reverse KL divergence is equivalent to finding an optimal policy. Our experimental results on MuJoCo-simulated environments and vision-based reaching tasks with a robotic arm show that ERIL is more sample-efficient than the baseline methods. We apply the method to human behaviors that perform a pole-balancing task and describe how the estimated reward functions show how every subject achieves her goal.

Dongqi Han, Kenji Doya, Jun Tani

In partially observable (PO) environments, deep reinforcement learning (RL) agents often suffer from unsatisfactory performance, since two problems need to be tackled together: how to extract information from the raw observations to solve the task, and how to improve the policy. In this study, we propose an RL algorithm for solving PO tasks. Our method comprises two parts: a variational recurrent model (VRM) for modeling the environment, and an RL controller that has access to both the environment and the VRM. The proposed algorithm was tested in two types of PO robotic control tasks, those in which either coordinates or velocities were not observable and those that require long-term memorization. Our experiments show that the proposed algorithm achieved better data efficiency and/or learned more optimal policy than other alternative approaches in tasks in which unobserved states cannot be inferred from raw observations in a simple manner.

Henrik Skibbe, Akiya Watakabe, Ken Nakae et al.

Understanding the connectivity in the brain is an important prerequisite for understanding how the brain processes information. In the Brain/MINDS project, a connectivity study on marmoset brains uses two-photon microscopy fluorescence images of axonal projections to collect the neuron connectivity from defined brain regions at the mesoscopic scale. The processing of the images requires the detection and segmentation of the axonal tracer signal. The objective is to detect as much tracer signal as possible while not misclassifying other background structures as the signal. This can be challenging because of imaging noise, a cluttered image background, distortions or varying image contrast cause problems. We are developing MarmoNet, a pipeline that processes and analyzes tracer image data of the common marmoset brain. The pipeline incorporates state-of-the-art machine learning techniques based on artificial convolutional neural networks (CNN) and image registration techniques to extract and map all relevant information in a robust manner. The pipeline processes new images in a fully automated way. This report introduces the current state of the tracer signal analysis part of the pipeline.

Tadashi Kozuno, Dongqi Han, Kenji Doya

In real-world applications of reinforcement learning (RL), noise from inherent stochasticity of environments is inevitable. However, current policy evaluation algorithms, which plays a key role in many RL algorithms, are either prone to noise or inefficient. To solve this issue, we introduce a novel policy evaluation algorithm, which we call Gap-increasing RetrAce Policy Evaluation (GRAPE). It leverages two recent ideas: (1) gap-increasing value update operators in advantage learning for noise-tolerance and (2) off-policy eligibility trace in Retrace algorithm for efficient learning. We provide detailed theoretical analysis of the new algorithm that shows its efficiency and noise-tolerance inherited from Retrace and advantage learning. Furthermore, our analysis shows that GRAPE's learning is significantly efficient than that of a simple learning-rate-based approach while keeping the same level of noise-tolerance. We applied GRAPE to control problems and obtained experimental results supporting our theoretical analysis.

Paavo Parmas, Carl Edward Rasmussen, Jan Peters et al.

Previously, the exploding gradient problem has been explained to be central in deep learning and model-based reinforcement learning, because it causes numerical issues and instability in optimization. Our experiments in model-based reinforcement learning imply that the problem is not just a numerical issue, but it may be caused by a fundamental chaos-like nature of long chains of nonlinear computations. Not only do the magnitudes of the gradients become large, the direction of the gradients becomes essentially random. We show that reparameterization gradients suffer from the problem, while likelihood ratio gradients are robust. Using our insights, we develop a model-based policy search framework, Probabilistic Inference for Particle-Based Policy Search (PIPPS), which is easily extensible, and allows for almost arbitrary models and policies, while simultaneously matching the performance of previous data-efficient learning algorithms. Finally, we invent the total propagation algorithm, which efficiently computes a union over all pathwise derivative depths during a single backwards pass, automatically giving greater weight to estimators with lower variance, sometimes improving over reparameterization gradients by $10^6$ times.

Dongqi Han, Kenji Doya, Jun Tani

Recurrent neural networks (RNNs) for reinforcement learning (RL) have shown distinct advantages, e.g., solving memory-dependent tasks and meta-learning. However, little effort has been spent on improving RNN architectures and on understanding the underlying neural mechanisms for performance gain. In this paper, we propose a novel, multiple-timescale, stochastic RNN for RL. Empirical results show that the network can autonomously learn to abstract sub-goals and can self-develop an action hierarchy using internal dynamics in a challenging continuous control task. Furthermore, we show that the self-developed compositionality of the network enhances faster re-learning when adapting to a new task that is a re-composition of previously learned sub-goals, than when starting from scratch. We also found that improved performance can be achieved when neural activities are subject to stochastic rather than deterministic dynamics.

Stefan Elfwing, Eiji Uchibe, Kenji Doya

We proposed the expected energy-based restricted Boltzmann machine (EE-RBM) as a discriminative RBM method for classification. Two characteristics of the EE-RBM are that the output is unbounded and that the target value of correct classification is set to a value much greater than one. In this study, by adopting features of the EE-RBM approach to feed-forward neural networks, we propose the UnBounded output network (UBnet) which is characterized by three features: (1) unbounded output units; (2) the target value of correct classification is set to a value much greater than one; and (3) the models are trained by a modified mean-squared error objective. We evaluate our approach using the MNIST, CIFAR-10, and CIFAR-100 benchmark datasets. We first demonstrate, for shallow UBnets on MNIST, that a setting of the target value equal to the number of hidden units significantly outperforms a setting of the target value equal to one, and it also outperforms standard neural networks by about 25\%. We then validate our approach by achieving high-level classification performance on the three datasets using unbounded output residual networks. We finally use MNIST to analyze the learned features and weights, and we demonstrate that UBnets are much more robust against adversarial examples than the standard approach of using a softmax output layer and training the networks by a cross-entropy objective.

Tadashi Kozuno, Eiji Uchibe, Kenji Doya

Approximate dynamic programming algorithms, such as approximate value iteration, have been successfully applied to many complex reinforcement learning tasks, and a better approximate dynamic programming algorithm is expected to further extend the applicability of reinforcement learning to various tasks. In this paper we propose a new, robust dynamic programming algorithm that unifies value iteration, advantage learning, and dynamic policy programming. We call it generalized value iteration (GVI) and its approximated version, approximate GVI (AGVI). We show AGVI's performance guarantee, which includes performance guarantees for existing algorithms, as special cases. We discuss theoretical weaknesses of existing algorithms, and explain the advantages of AGVI. Numerical experiments in a simple environment support theoretical arguments, and suggest that AGVI is a promising alternative to previous algorithms.

Stefan Elfwing, Eiji Uchibe, Kenji Doya

The efficiency of reinforcement learning algorithms depends critically on a few meta-parameters that modulates the learning updates and the trade-off between exploration and exploitation. The adaptation of the meta-parameters is an open question in reinforcement learning, which arguably has become more of an issue recently with the success of deep reinforcement learning in high-dimensional state spaces. The long learning times in domains such as Atari 2600 video games makes it not feasible to perform comprehensive searches of appropriate meta-parameter values. We propose the Online Meta-learning by Parallel Algorithm Competition (OMPAC) method. In the OMPAC method, several instances of a reinforcement learning algorithm are run in parallel with small differences in the initial values of the meta-parameters. After a fixed number of episodes, the instances are selected based on their performance in the task at hand. Before continuing the learning, Gaussian noise is added to the meta-parameters with a predefined probability. We validate the OMPAC method by improving the state-of-the-art results in stochastic SZ-Tetris and in standard Tetris with a smaller, 10$\times$10, board, by 31% and 84%, respectively, and by improving the results for deep Sarsa($λ$) agents in three Atari 2600 games by 62% or more. The experiments also show the ability of the OMPAC method to adapt the meta-parameters according to the learning progress in different tasks.

Stefan Elfwing, Eiji Uchibe, Kenji Doya

In recent years, neural networks have enjoyed a renaissance as function approximators in reinforcement learning. Two decades after Tesauro's TD-Gammon achieved near top-level human performance in backgammon, the deep reinforcement learning algorithm DQN achieved human-level performance in many Atari 2600 games. The purpose of this study is twofold. First, we propose two activation functions for neural network function approximation in reinforcement learning: the sigmoid-weighted linear unit (SiLU) and its derivative function (dSiLU). The activation of the SiLU is computed by the sigmoid function multiplied by its input. Second, we suggest that the more traditional approach of using on-policy learning with eligibility traces, instead of experience replay, and softmax action selection with simple annealing can be competitive with DQN, without the need for a separate target network. We validate our proposed approach by, first, achieving new state-of-the-art results in both stochastic SZ-Tetris and Tetris with a small 10$\times$10 board, using TD($λ$) learning and shallow dSiLU network agents, and, then, by outperforming DQN in the Atari 2600 domain by using a deep Sarsa($λ$) agent with SiLU and dSiLU hidden units.

Tomoki Tokuda, Junichiro Yoshimoto, Yu Shimizu et al.

We propose a novel method for multiple clustering that assumes a co-clustering structure (partitions in both rows and columns of the data matrix) in each view. The new method is applicable to high-dimensional data. It is based on a nonparametric Bayesian approach in which the number of views and the number of feature-/subject clusters are inferred in a data-driven manner. We simultaneously model different distribution families, such as Gaussian, Poisson, and multinomial distributions in each cluster block. This makes our method applicable to datasets consisting of both numerical and categorical variables, which biomedical data typically do. Clustering solutions are based on variational inference with mean field approximation. We apply the proposed method to synthetic and real data, and show that our method outperforms other multiple clustering methods both in recovering true cluster structures and in computation time. Finally, we apply our method to a depression dataset with no true cluster structure available, from which useful inferences are drawn about possible clustering structures of the data.