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 Markov Models


A Generalist Hanabi Agent

arXiv.org Artificial Intelligence

Traditional multi-agent reinforcement learning (MARL) systems can develop cooperative strategies through repeated interactions. However, these systems are unable to perform well on any other setting than the one they have been trained on, and struggle to successfully cooperate with unfamiliar collaborators. This is particularly visible in the Hanabi benchmark, a popular 2-to-5 player cooperative card-game which requires complex reasoning and precise assistance to other agents. Current MARL agents for Hanabi can only learn one specific game-setting (e.g., 2-player games), and play with the same algorithmic agents. This is in stark contrast to humans, who can quickly adjust their strategies to work with unfamiliar partners or situations. In this paper, we introduce Recurrent Replay Relevance Distributed DQN (R3D2), a generalist agent for Hanabi, designed to overcome these limitations. We reformulate the task using text, as language has been shown to improve transfer. We then propose a distributed MARL algorithm that copes with the resulting dynamic observation-and action-space. In doing so, our agent is the first that can play all game settings concurrently, and extend strategies learned from one setting to other ones. As a consequence, our agent also demonstrates the ability to collaborate with different algorithmic agents -- agents that are themselves unable to do so. Humans were able to thrive as a society through their ability to cooperate. Interactions among multiple people or agents are essential components of various aspects of our lives, ranging from everyday activities like commuting to work, to the functioning of fundamental institutions like governments and economic markets. Through repeated interactions, humans can understand their partners, and learn to reason from their perspective. Crucially, humans can generalize their reasonings towards novel partners, in different situations. Artificial agents should be able to do the same for the successful collaboration of artificial and hybrid systems (Dafoe et al., 2020). This is why defining the problem of multi-agent cooperation nicely fits the multi-agent reinforcement learning (MARL) paradigm, as artificial agents learn to collaborate together through repeated interactions, in the same principled manner humans would. In MARL, the game of Hanabi has emerged as a popular benchmark to assess the cooperative abilities of learning agents (Bard et al., 2020).


Second-order Theory of Mind for Human Teachers and Robot Learners

arXiv.org Artificial Intelligence

Confusing or otherwise unhelpful learner feedback creates or perpetuates erroneous beliefs that the teacher and learner have of each other, thereby increasing the cognitive burden placed upon the human teacher. For example, the robot's feedback might cause the human to misunderstand what the learner knows about the learning objective or how the learner learns. At the same time -- and in addition to the learning objective -- the learner might misunderstand how the teacher perceives the learner's task knowledge and learning processes. To ease the teaching burden, the learner should provide feedback that accounts for these misunderstandings and elicits efficient teaching from the human. This work endows an AI learner with a Second-order Theory of Mind that models perceived rationality as a source for the erroneous beliefs a teacher and learner may have of one another. It also explores how a learner can ease the teaching burden and improve teacher efficacy if it selects feedback which accounts for its model of the teacher's beliefs about the learner and its learning objective.


Disentangling Fine-Tuning from Pre-Training in Visual Captioning with Hybrid Markov Logic

arXiv.org Artificial Intelligence

Multimodal systems have highly complex processing pipelines and are pretrained over large datasets before being fine-tuned for specific tasks such as visual captioning. However, it becomes hard to disentangle what the model learns during the fine-tuning process from what it already knows due to its pretraining. In this work, we learn a probabilistic model using Hybrid Markov Logic Networks (HMLNs) over the training examples by relating symbolic knowledge (extracted from the caption) with visual features (extracted from the image). For a generated caption, we quantify the influence of training examples based on the HMLN distribution using probabilistic inference. We evaluate two types of inference procedures on the MSCOCO dataset for different types of captioning models. Our results show that for BLIP2 (a model that uses a LLM), the fine-tuning may have smaller influence on the knowledge the model has acquired since it may have more general knowledge to perform visual captioning as compared to models that do not use a LLM


Deep Belief Markov Models for POMDP Inference

arXiv.org Artificial Intelligence

This work introduces a novel deep learning-based architecture, termed the Deep Belief Markov Model (DBMM), which provides efficient, model-formulation agnostic inference in Partially Observable Markov Decision Process (POMDP) problems. The POMDP framework allows for modeling and solving sequential decision-making problems under observation uncertainty. In complex, high-dimensional, partially observable environments, existing methods for inference based on exact computations (e.g., via Bayes' theorem) or sampling algorithms do not scale well. Furthermore, ground truth states may not be available for learning the exact transition dynamics. DBMMs extend deep Markov models into the partially observable decision-making framework and allow efficient belief inference entirely based on available observation data via variational inference methods. By leveraging the potency of neural networks, DBMMs can infer and simulate non-linear relationships in the system dynamics and naturally scale to problems with high dimensionality and discrete or continuous variables. In addition, neural network parameters can be dynamically updated efficiently based on data availability. DBMMs can thus be used to infer a belief variable, thus enabling the derivation of POMDP solutions over the belief space. We evaluate the efficacy of the proposed methodology by evaluating the capability of model-formulation agnostic inference of DBMMs in benchmark problems that include discrete and continuous variables.


Sampling Decisions

arXiv.org Machine Learning

In this manuscript we introduce a novel Decision Flow (DF) framework for sampling from a target distribution while incorporating additional guidance from a prior sampler. DF can be viewed as an AI driven algorithmic reincarnation of the Markov Decision Process (MDP) approach in Stochastic Optimal Control. It extends the continuous space, continuous time path Integral Diffusion sampling technique to discrete time and space, while also generalizing the Generative Flow Network framework. In its most basic form, an explicit, Neural Network (NN) free formulation, DF leverages the linear solvability of the the underlying MDP to adjust the transition probabilities of the prior sampler. The resulting Markov Process is expressed as a convolution of the reverse time Green's function of the prior sampling with the target distribution. We illustrate the DF framework through an example of sampling from the Ising model, discuss potential NN based extensions, and outline how DF can enhance guided sampling across various applications.


Estimating stationary mass, frequency by frequency

arXiv.org Machine Learning

Suppose we observe a trajectory of length $n$ from an $\alpha$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary distribution of any such process on elements that occur with a certain frequency in the observed sequence. We estimate this vector of probabilities in total variation distance, showing universal consistency in $n$ and recovering known results for i.i.d. sequences as special cases. Our proposed methodology carefully combines the plug-in (or empirical) estimator with a recently-proposed modification of the Good--Turing estimator called WingIt, which was originally developed for Markovian sequences. En route to controlling the error of our estimator, we develop new performance bounds on WingIt and the plug-in estimator for $\alpha$-mixing stochastic processes. Importantly, the extensively used method of Poissonization can no longer be applied in our non i.i.d. setting, and so we develop complementary tools -- including concentration inequalities for a natural self-normalized statistic of mixing sequences -- that may prove independently useful in the design and analysis of estimators for related problems.


Probabilistic Shielding for Safe Reinforcement Learning

arXiv.org Machine Learning

In real-life scenarios, a Reinforcement Learning (RL) agent aiming to maximise their reward, must often also behave in a safe manner, including at training time. Thus, much attention in recent years has been given to Safe RL, where an agent aims to learn an optimal policy among all policies that satisfy a given safety constraint. However, strict safety guarantees are often provided through approaches based on linear programming, and thus have limited scaling. In this paper we present a new, scalable method, which enjoys strict formal guarantees for Safe RL, in the case where the safety dynamics of the Markov Decision Process (MDP) are known, and safety is defined as an undiscounted probabilistic avoidance property. Our approach is based on state-augmentation of the MDP, and on the design of a shield that restricts the actions available to the agent. We show that our approach provides a strict formal safety guarantee that the agent stays safe at training and test time. Furthermore, we demonstrate that our approach is viable in practice through experimental evaluation.


TERL: Large-Scale Multi-Target Encirclement Using Transformer-Enhanced Reinforcement Learning

arXiv.org Artificial Intelligence

Pursuit-evasion (PE) problem is a critical challenge in multi-robot systems (MRS). While reinforcement learning (RL) has shown its promise in addressing PE tasks, research has primarily focused on single-target pursuit, with limited exploration of multi-target encirclement, particularly in large-scale settings. This paper proposes a Transformer-Enhanced Reinforcement Learning (TERL) framework for large-scale multi-target encirclement. By integrating a transformer-based policy network with target selection, TERL enables robots to adaptively prioritize targets and safely coordinate robots. Results show that TERL outperforms existing RL-based methods in terms of encirclement success rate and task completion time, while maintaining good performance in large-scale scenarios. Notably, TERL, trained on small-scale scenarios (15 pursuers, 4 targets), generalizes effectively to large-scale settings (80 pursuers, 20 targets) without retraining, achieving a 100% success rate.


APF+: Boosting adaptive-potential function reinforcement learning methods with a W-shaped network for high-dimensional games

arXiv.org Artificial Intelligence

Studies in reward shaping for reinforcement learning (RL) have flourished in recent years due to its ability to speed up training. Our previous work proposed an adaptive potential function (APF) and showed that APF can accelerate the Q-learning with a Multi-layer Perceptron algorithm in the low-dimensional domain. This paper proposes to extend APF with an encoder (APF+) for RL state representation, allowing applying APF to the pixel-based Atari games using a state-encoding method that projects high-dimensional game's pixel frames to low-dimensional embeddings. We approach by designing the state-representation encoder as a W-shaped network (W-Net), by using which we are able to encode both the background as well as the moving entities in the game frames. Specifically, the embeddings derived from the pre-trained W-Net consist of two latent vectors: One represents the input state, and the other represents the deviation of the input state's representation from itself. We then incorporate W-Net into APF to train a downstream Dueling Deep Q-Network (DDQN), obtain the APF-WNet-DDQN, and demonstrate its effectiveness in Atari game-playing tasks. To evaluate the APF+W-Net module in such high-dimensional tasks, we compare with two types of baseline methods: (i) the basic DDQN; and (ii) two encoder-replaced APF-DDQN methods where we replace W-Net by (a) an unsupervised state representation method called Spatiotemporal Deep Infomax (ST-DIM) and (b) a ground truth state representation provided by the Atari Annotated RAM Interface (ARI). The experiment results show that out of 20 Atari games, APF-WNet-DDQN outperforms DDQN (14/20 games) and APF-STDIM-DDQN (13/20 games) significantly. In comparison against the APF-ARI-DDQN which employs embeddings directly of the detailed game-internal state information, the APF-WNet-DDQN achieves a comparable performance.


Decentralized Hidden Markov Modeling with Equal Exit Probabilities

arXiv.org Artificial Intelligence

Social learning strategies enable agents to infer the underlying true state of nature in a distributed manner by receiving private environmental signals and exchanging beliefs with their neighbors. Previous studies have extensively focused on static environments, where the underlying true state remains unchanged over time. In this paper, we consider a dynamic setting where the true state evolves according to a Markov chain with equal exit probabilities. Based on this assumption, we present a social learning strategy for dynamic environments, termed Diffusion $\alpha$-HMM. By leveraging a simplified parameterization, we derive a nonlinear dynamical system that governs the evolution of the log-belief ratio over time. This formulation further reveals the relationship between the linearized form of Diffusion $\alpha$-HMM and Adaptive Social Learning, a well-established social learning strategy for dynamic environments. Furthermore, we analyze the convergence and fixed-point properties of a reference system, providing theoretical guarantees on the learning performance of the proposed algorithm in dynamic settings. Numerical experiments compare various distributed social learning strategies across different dynamic environments, demonstrating the impact of nonlinearity and parameterization on learning performance in a range of dynamic scenarios.