Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming paradigm enables end-to-end differentiation of complex computer programs (including those with control flows and data structures), making gradient-based optimization of program parameters possible. As an emerging paradigm, differentiable programming builds upon several areas of computer science and applied mathematics, including automatic differentiation, graphical models, optimization and statistics. This book presents a comprehensive review of the fundamental concepts useful for differentiable programming. We adopt two main perspectives, that of optimization and that of probability, with clear analogies between the two. Differentiable programming is not merely the differentiation of programs, but also the thoughtful design of programs intended for differentiation. By making programs differentiable, we inherently introduce probability distributions over their execution, providing a means to quantify the uncertainty associated with program outputs.

The management of mixed traffic that consists of robot vehicles (RVs) and human-driven vehicles (HVs) at complex intersections presents a multifaceted challenge. Traditional signal controls often struggle to adapt to dynamic traffic conditions and heterogeneous vehicle types. Recent advancements have turned to strategies based on reinforcement learning (RL), leveraging its model-free nature, real-time operation, and generalizability over different scenarios. We introduce a hierarchical RL framework to manage mixed traffic through precise longitudinal and lateral control of RVs. Our proposed hierarchical framework combines the state-of-the-art mixed traffic control algorithm as a high level decision maker to improve the performance and robustness of the whole system. Our experiments demonstrate that the framework can reduce the average waiting time by up to 54% compared to the state-of-the-art mixed traffic control method. When the RV penetration rate exceeds 60%, our technique consistently outperforms conventional traffic signal control programs in terms of the average waiting time for all vehicles at the intersection.

Safe and efficient object manipulation is a key enabler of many real-world robot applications. However, this is challenging because robot operation must be robust to a range of sensor and actuator uncertainties. In this paper, we present a physics-informed causal-inference-based framework for a robot to probabilistically reason about candidate actions in a block stacking task in a partially observable setting. We integrate a physics-based simulation of the rigid-body system dynamics with a causal Bayesian network (CBN) formulation to define a causal generative probabilistic model of the robot decision-making process. Using simulation-based Monte Carlo experiments, we demonstrate our framework's ability to successfully: (1) predict block tower stability with high accuracy (Pred Acc: 88.6%); and, (2) select an approximate next-best action for the block stacking task, for execution by an integrated robot system, achieving 94.2% task success rate. We also demonstrate our framework's suitability for real-world robot systems by demonstrating successful task executions with a domestic support robot, with perception and manipulation sub-system integration. Hence, we show that by embedding physics-based causal reasoning into robots' decision-making processes, we can make robot task execution safer, more reliable, and more robust to various types of uncertainty.

Policy Mirror Descent (PMD) stands as a versatile algorithmic framework encompassing several seminal policy gradient algorithms such as natural policy gradient, with connections with state-of-the-art reinforcement learning (RL) algorithms such as TRPO and PPO. PMD can be seen as a soft Policy Iteration algorithm implementing regularized 1-step greedy policy improvement. However, 1-step greedy policies might not be the best choice and recent remarkable empirical successes in RL such as AlphaGo and AlphaZero have demonstrated that greedy approaches with respect to multiple steps outperform their 1-step counterpart. In this work, we propose a new class of PMD algorithms called $h$-PMD which incorporates multi-step greedy policy improvement with lookahead depth $h$ to the PMD update rule. To solve discounted infinite horizon Markov Decision Processes with discount factor $\gamma$, we show that $h$-PMD which generalizes the standard PMD enjoys a faster dimension-free $\gamma^h$-linear convergence rate, contingent on the computation of multi-step greedy policies. We propose an inexact version of $h$-PMD where lookahead action values are estimated. Under a generative model, we establish a sample complexity for $h$-PMD which improves over prior work. Finally, we extend our result to linear function approximation to scale to large state spaces. Under suitable assumptions, our sample complexity only involves dependence on the dimension of the feature map space instead of the state space size.

We present a general framework for applying learning algorithms and heuristical guidance to the verification of Markov decision processes (MDPs). The primary goal of our techniques is to improve performance by avoiding an exhaustive exploration of the state space, instead focussing on particularly relevant areas of the system, guided by heuristics. Our work builds on the previous results of Br{\'{a}}zdil et al., significantly extending it as well as refining several details and fixing errors. The presented framework focuses on probabilistic reachability, which is a core problem in verification, and is instantiated in two distinct scenarios. The first assumes that full knowledge of the MDP is available, in particular precise transition probabilities. It performs a heuristic-driven partial exploration of the model, yielding precise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP without knowing the exact transition dynamics. Here, we obtain probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stopping criteria for the approximation. In particular, the latter is an extension of statistical model-checking (SMC) for unbounded properties in MDPs. In contrast to other related approaches, we do not restrict our attention to time-bounded (finite-horizon) or discounted properties, nor assume any particular structural properties of the MDP.

This paper presents a novel reinforcement learning (RL) approach called HAAM-RL (Heuristic Algorithm-based Action Masking Reinforcement Learning) for optimizing the color batching re-sequencing problem in automobile painting processes. The existing heuristic algorithms have limitations in adequately reflecting real-world constraints and accurately predicting logistics performance. Our methodology incorporates several key techniques including a tailored Markov Decision Process (MDP) formulation, reward setting including Potential-Based Reward Shaping, action masking using heuristic algorithms (HAAM-RL), and an ensemble inference method that combines multiple RL models. The RL agent is trained and evaluated using FlexSim, a commercial 3D simulation software, integrated with our RL MLOps platform BakingSoDA. Experimental results across 30 scenarios demonstrate that HAAM-RL with an ensemble inference method achieves a 16.25% performance improvement over the conventional heuristic algorithm, with stable and consistent results. The proposed approach exhibits superior performance and generalization capability, indicating its effectiveness in optimizing complex manufacturing processes. The study also discusses future research directions, including alternative state representations, incorporating model-based RL methods, and integrating additional real-world constraints.

Defining and thereby separating the intelligent "agent" from its embodied "environment", which then provides feedback to the agent, is crucial to model intelligent behaviour. Popular approaches, like reinforcement learning (RL), heavily employ such models containing agent-environment loops, which boils down the problem to agent(s) trying to maximise reward in the given uncertain environment Sutton and Barto [2018]. Active inference has emerged in neuroscience as a biologically plausible framework Friston [2010], which adopts a different approach to modelling intelligent behaviour compared to other contemporary methods like RL. In the active inference framework, an agent accumulates and maximises the model evidence during its lifetime to perceive, learn, and make decisions Da Costa et al. [2020], Sajid et al. [2021], Millidge et al. [2020]. However, maximising the model evidence becomes challenging when the agent encounters a highly'entropic' observation (i.e. an unexpected observation) concerning the agent's generative (world) model Da Costa et al. [2020], Sajid et al. [2021], Millidge et al. [2020]. This seemingly intractable objective of maximising model evidence (or minimising the entropy of encountered observations) is achievable by minimising an upper bound on the entropy of observations, called variational free energy Da Costa et al. [2020], Sajid et al. [2021]. Given this general foundation, active inference Friston et al. [2017] offers excellent flexibility in defining the generative model structure for a given problem and has attracted much attention in various domainsKuchling et al. [2020], Deane et al. [2020]. In this work, we develop an efficient decision-making scheme based on active inference by combining'planning' and'learning from experience'.

In this paper we consider a transformer with an $n$-gram structure, such as the one underlying ChatGPT. The transformer provides next word probabilities, which can be used to generate word sequences. We consider methods for computing word sequences that are highly likely, based on these probabilities. Computing the optimal (i.e., most likely) word sequence starting with a given initial state is an intractable problem, so we propose methods to compute highly likely sequences of $N$ words in time that is a low order polynomial in $N$ and in the vocabulary size of the $n$-gram. These methods are based on the rollout approach from approximate dynamic programming, a form of single policy iteration, which can improve the performance of any given heuristic policy. In our case we use a greedy heuristic that generates as next word one that has the highest probability. We show with analysis, examples, and computational experimentation that our methods are capable of generating highly likely sequences with a modest increase in computation over the greedy heuristic. While our analysis and experiments are focused on Markov chains of the type arising in transformer and ChatGPT-like models, our methods apply to general finite-state Markov chains, and related inference applications of Hidden Markov Models (HMM), where Viterbi decoding is used extensively.

Scanpath classification is an area in eye tracking research with possible applications in medicine, manufacturing as well as training systems for students in various domains. In this paper we propose a trainable feature extraction module for deep neural networks. The purpose of this module is to transform a scanpath into a feature vector which is directly useable for the deep neural network architecture. Based on the backpropagated error of the deep neural network, the feature extraction module adapts its parameters to improve the classification performance. Therefore, our feature extraction module is jointly trainable with the deep neural network. The motivation to this feature extraction module is based on classical histogram-based approaches which usually compute distributions over a scanpath. We evaluated our module on three public datasets and compared it to the state of the art approaches.

Robot arms should be able to learn new tasks. One framework here is reinforcement learning, where the robot is given a reward function that encodes the task, and the robot autonomously learns actions to maximize its reward. Existing approaches to reinforcement learning often frame this problem as a Markov decision process, and learn a policy (or a hierarchy of policies) to complete the task. These policies reason over hundreds of fine-grained actions that the robot arm needs to take: e.g., moving slightly to the right or rotating the end-effector a few degrees. But the manipulation tasks that we want robots to perform can often be broken down into a small number of high-level motions: e.g., reaching an object or turning a handle. In this paper we therefore propose a waypoint-based approach for model-free reinforcement learning. Instead of learning a low-level policy, the robot now learns a trajectory of waypoints, and then interpolates between those waypoints using existing controllers. Our key novelty is framing this waypoint-based setting as a sequence of multi-armed bandits: each bandit problem corresponds to one waypoint along the robot's motion. We theoretically show that an ideal solution to this reformulation has lower regret bounds than standard frameworks. We also introduce an approximate posterior sampling solution that builds the robot's motion one waypoint at a time. Results across benchmark simulations and two real-world experiments suggest that this proposed approach learns new tasks more quickly than state-of-the-art baselines. See videos here: https://youtu.be/MMEd-lYfq4Y