A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated the effective particles are, and the quicker and more accurate it is to approximate the hidden Markov model, especially for the nonlinear case. We propose a repetitive deterministic domain with median ergodicity for resampling and have achieved the lowest variances compared to the other resampling methods. As the size of the deterministic domain $M\ll N$ (the size of population), given a feasible size of particles, our algorithm is faster than the state of the art, which is verified by theoretical deduction and experiments of a hidden Markov model in both the linear and non-linear cases.

Optimizing for humans' latent preferences remains a grand challenge in route recommendation. Prior research has provided increasingly general techniques based on inverse reinforcement learning (IRL), yet no approach has been successfully scaled to world-sized routing problems with hundreds of millions of states and demonstration trajectories. In this paper, we provide methods for scaling IRL using graph compression, spatial parallelization, and problem initialization based on dominant eigenvectors. We revisit classic algorithms and study them in a large-scale setting, and make the key observation that there exists a trade-off between the use of cheap, deterministic planners and expensive yet robust stochastic policies. We leverage this insight in Receding Horizon Inverse Planning (RHIP), a new generalization of classic IRL algorithms that provides fine-grained control over performance trade-offs via its planning horizon. Our contributions culminate in a policy that achieves a 16-24% improvement in global route quality, and to the best of our knowledge, represents the largest instance of IRL in a real-world setting to date. Benchmark results show critical benefits to more sustainable modes of transportation, where factors beyond journey time play a substantial role. We conclude by conducting an ablation study of key components, presenting negative results from alternative eigenvalue solvers, and identifying opportunities to further improve scalability via IRL-specific batching strategies.

Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses randomly taking small steps within uncertain regions in the parameter space. We are the first to consider the posterior distribution of the objective as a mapping of samples in an infinite-dimensional Euclidean space where deterministic submanifolds are embedded and propose a new criterion by maximizing the weighted Riesz polarization quantity, to discretize rectifiable submanifolds via pairwise interaction. We study the characteristics of Chebyshev particles and embed them into sequential MCMC, a novel sampler with a high acceptance ratio that proposes only a few evaluations. We have achieved high performance from the experiments for parameter inference in a linear Gaussian state-space model with synthetic data and a non-linear stochastic volatility model with real-world data.

The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of optimal control. The main contributions firstly concern properties of the relaxation, described as a deterministic convex program: we identify conditions for a bounded solution, and a significant relationship between the solution to the new convex program, and the solution to standard Q-learning. The second set of contributions concern algorithm design and analysis: (i) A direct model-free method for approximating the convex program for Q-learning shares properties with its ideal. In particular, a bounded solution is ensured subject to a simple property of the basis functions; (ii) The proposed algorithms are convergent and new techniques are introduced to obtain the rate of convergence in a mean-square sense; (iii) The approach can be generalized to a range of performance criteria, and it is found that variance can be reduced by considering ``relative'' dynamic programming equations; (iv) The theory is illustrated with an application to a classical inventory control problem.

Monitoring drivers' mental workload facilitates initiating and maintaining safe interactions with in-vehicle information systems, and thus delivers adaptive human machine interaction with reduced impact on the primary task of driving. In this paper, we tackle the problem of workload estimation from driving performance data. First, we present a novel on-road study for collecting subjective workload data via a modified peripheral detection task in naturalistic settings. Key environmental factors that induce a high mental workload are identified via video analysis, e.g. junctions and behaviour of vehicle in front. Second, a supervised learning framework using state-of-the-art time series classifiers (e.g. convolutional neural network and transform techniques) is introduced to profile drivers based on the average workload they experience during a journey. A Bayesian filtering approach is then proposed for sequentially estimating, in (near) real-time, the driver's instantaneous workload. This computationally efficient and flexible method can be easily personalised to a driver (e.g. incorporate their inferred average workload profile), adapted to driving/environmental contexts (e.g. road type) and extended with data streams from new sources. The efficacy of the presented profiling and instantaneous workload estimation approaches are demonstrated using the on-road study data, showing $F_{1}$ scores of up to 92% and 81%, respectively.

Control barrier functions (CBFs) enable guaranteed safe multi-agent navigation in the continuous domain. The resulting navigation performance, however, is highly sensitive to the underlying hyperparameters. Traditional approaches consider fixed CBFs (where parameters are tuned apriori), and hence, typically do not perform well in cluttered and highly dynamic environments: conservative parameter values can lead to inefficient agent trajectories, or even failure to reach goal positions, whereas aggressive parameter values can lead to infeasible controls. To overcome these issues, in this paper, we propose online CBFs, whereby hyperparameters are tuned in real-time, as a function of what agents perceive in their immediate neighborhood. Since the explicit relationship between CBFs and navigation performance is hard to model, we leverage reinforcement learning to learn CBF-tuning policies in a model-free manner. Because we parameterize the policies with graph neural networks (GNNs), we are able to synthesize decentralized agent controllers that adjust parameter values locally, varying the degree of conservative and aggressive behaviors across agents. Simulations as well as real-world experiments show that (i) online CBFs are capable of solving navigation scenarios that are infeasible for fixed CBFs, and (ii), that they improve navigation performance by adapting to other agents and changes in the environment.

Acceptance-rejection (AR), Independent Metropolis Hastings (IMH) or importance sampling (IS) Monte Carlo (MC) simulation algorithms all involve computing ratios of probability density functions (pdfs). On the other hand, classifiers discriminate labeled samples produced by a mixture of two distributions and can be used for approximating the ratio of the two corresponding pdfs.This bridge between simulation and classification enables us to propose pdf-free versions of pdf-ratio-based simulation algorithms, where the ratio is replaced by a surrogate function computed via a classifier. From a probabilistic modeling perspective, our procedure involves a structured energy based model which can easily be trained and is compatible with the classical samplers.

Coverage path planning (CPP) is a critical problem in robotics, where the goal is to find an efficient path that covers every point in an area of interest. This work addresses the power-constrained CPP problem with recharge for battery-limited unmanned aerial vehicles (UAVs). In this problem, a notable challenge emerges from integrating recharge journeys into the overall coverage strategy, highlighting the intricate task of making strategic, long-term decisions. We propose a novel proximal policy optimization (PPO)-based deep reinforcement learning (DRL) approach with map-based observations, utilizing action masking and discount factor scheduling to optimize coverage trajectories over the entire mission horizon. We further provide the agent with a position history to handle emergent state loops caused by the recharge capability. Our approach outperforms a baseline heuristic, generalizes to different target zones and maps, with limited generalization to unseen maps. We offer valuable insights into DRL algorithm design for long-horizon problems and provide a publicly available software framework for the CPP problem.

Reinforcement learning algorithms often require finiteness of state and action spaces in Markov decision processes (MDPs) (also called controlled Markov chains) and various efforts have been made in the literature towards the applicability of such algorithms for continuous state and action spaces. In this paper, we show that under very mild regularity conditions (in particular, involving only weak continuity of the transition kernel of an MDP), Q-learning for standard Borel MDPs via quantization of states and actions (called Quantized Q-Learning) converges to a limit, and furthermore this limit satisfies an optimality equation which leads to near optimality with either explicit performance bounds or which are guaranteed to be asymptotically optimal. Our approach builds on (i) viewing quantization as a measurement kernel and thus a quantized MDP as a partially observed Markov decision process (POMDP), (ii) utilizing near optimality and convergence results of Q-learning for POMDPs, and (iii) finally, near-optimality of finite state model approximations for MDPs with weakly continuous kernels which we show to correspond to the fixed point of the constructed POMDP. Thus, our paper presents a very general convergence and approximation result for the applicability of Q-learning for continuous MDPs.

Triplet Markov chains are general generative models for sequential data which take into account three kinds of random variables: (noisy) observations, their associated discrete labels and latent variables which aim at strengthening the distribution of the observations and their associated labels. However, in practice, we do not have at our disposal all the labels associated to the observations to estimate the parameters of such models. In this paper, we propose a general framework based on a variational Bayesian inference to train parameterized triplet Markov chain models in a semi-supervised context. The generality of our approach enables us to derive semi-supervised algorithms for a variety of generative models for sequential Bayesian classification.