We propose techniques for efficiently determining optimal solutions to large logistics planning domain problems. We map a problem instance to a directed graph and show that no more than one vehicle per weakly connected component of the graph is needed for an optimal solution. We propose techniques for efficiently finding the vehicles which must be employed for an optimal solution. Also we develop a strong admissible heuristic based on the analysis of a directed graph, the cycles of which represent situations in the problem state in which a vehicle must visit a location more than once. To the best of our knowledge, ours is the first method that determines optimal solutions for large logistics instances (including the largest instances in the IPC 1998 and IPC 2000 problem sets).

A classical result in optimal search shows that A* with an admissible and consistent heuristic expands every state whose f-value is below the optimal solution cost and no state whose f-value is above the optimal solution cost. For satisficing search algorithms, a similarly clear understanding is currently lacking. We examine the search behaviour of greedy best-first search (gbfs) in order to make progress towards such an understanding. We introduce the concept of high-water mark benches, which separate the search space into areas that are searched by a gbfs algorithm in sequence. High-water mark benches allow us to exactly determine the set of states that are not expanded under any gbfs tie-breaking strategy. For the remaining states, we show that some are expanded by all gbfs searches, while others are expanded only if certain conditions are met.

Heuristic search is one of the most successful approaches to classical planning, finding solution paths in large state spaces. A major focus has been the development of domain-independent heuristic functions. One recent method are partial delete relaxation heuristics, improving over the standard delete relaxation heuristic through imposing a set C of conjunctions to be treated as atomic. Practical methods for selecting C are based on counter-example guided abstraction refinement, where iteratively a relaxed plan is checked for conflicts and new atomic conjunctions are introduced to address these. However, in each refinement step, the choice of possible new conjunctions is huge. The literature so far offers merely one simple strategy to make that choice. Here we fill that gap, considering a sizable space of basic ranking strategies as well as combinations thereof. We furthermore devise ranking strategies for conjunction-forgetting, where the ranking pertains to the current conjunctions and thus statistics over their usefulness can be maintained. Our experiments show that ranking strategies do make a large difference in performance, and that our new strategies can be useful.

Agent planning programs are finite-state programs, possibly containing loops, whose atomic instructions consist of a guard, a maintenance goal, and an achievement goal, which act as precondition-invariance-postcondition assertions in program specification. The execution of such programs requires generating plans that meet the goals specified in the atomic instructions, while respecting the program control flow. Recently, De Giacomo et al. (2016) presented a technique, based on iteratively solving classical planning problems with action costs, for realizing planning programs in deterministic domains. Such a technique works generally well for domains with no or very few dead-end states. In this paper, we propose an enhancement of this technique to handle deterministic domains that have potentially many dead-end states, and we study the effectiveness of our technique through an experimental analysis.

The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each time solving for the most likely configuration. We derive an entire family of related methods, of which the Gumbel trick is one member, and show that the new methods have superior properties in several settings with minimal additional computational cost. In particular, for the Gumbel trick to yield computational benefits for discrete graphical models, Gumbel perturbations on all configurations are typically replaced with so-called low-rank perturbations. We show how a subfamily of our new methods adapts to this setting, proving new upper and lower bounds on the log partition function and deriving a family of sequential samplers for the Gibbs distribution. Finally, we balance the discussion by showing how the simpler analytical form of the Gumbel trick enables additional theoretical results.

In this work, we attempt to ameliorate the impact of data sparsity in the context of session-based recommendation. Specifically, we seek to devise a machine learning mechanism capable of extracting subtle and complex underlying temporal dynamics in the observed session data, so as to inform the recommendation algorithm. To this end, we improve upon systems that utilize deep learning techniques with recurrently connected units; we do so by adopting concepts from the field of Bayesian statistics, namely variational inference. Our proposed approach consists in treating the network recurrent units as stochastic latent variables with a prior distribution imposed over them. On this basis, we proceed to infer corresponding posteriors; these can be used for prediction and recommendation generation, in a way that accounts for the uncertainty in the available sparse training data. To allow for our approach to easily scale to large real-world datasets, we perform inference under an approximate amortized variational inference (AVI) setup, whereby the learned posteriors are parameterized via (conventional) neural networks. We perform an extensive experimental evaluation of our approach using challenging benchmark datasets, and illustrate its superiority over existing state-of-the-art techniques.

Bayesian optimization (BO) methods are useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition function is built. This function guides the optimization process and measures the expected utility of performing an evaluation of the objective at a new point. GPs assume continous input variables. When this is not the case, such as when some of the input variables take integer values, one has to introduce extra approximations. A common approach is to round the suggested variable value to the closest integer before doing the evaluation of the objective. We show that this can lead to problems in the optimization process and describe a more principled approach to account for input variables that are integer-valued. We illustrate in both synthetic and a real experiments the utility of our approach, which significantly improves the results of standard BO methods on problems involving integer-valued variables. Keywords: Parameter tuning, Bayesian optimization, Gaussian processes, Integer-valued variables.

We present an efficient block-diagonal ap- proximation to the Gauss-Newton matrix for feedforward neural networks. Our result- ing algorithm is competitive against state- of-the-art first order optimisation methods, with sometimes significant improvement in optimisation performance. Unlike first-order methods, for which hyperparameter tuning of the optimisation parameters is often a labo- rious process, our approach can provide good performance even when used with default set- tings. A side result of our work is that for piecewise linear transfer functions, the net- work objective function can have no differ- entiable local maxima, which may partially explain why such transfer functions facilitate effective optimisation.

We explore a recently proposed Variational Dropout technique that provided an elegant Bayesian interpretation to Gaussian Dropout. We extend Variational Dropout to the case when dropout rates are unbounded, propose a way to reduce the variance of the gradient estimator and report first experimental results with individual dropout rates per weight. Interestingly, it leads to extremely sparse solutions both in fully-connected and convolutional layers. This effect is similar to automatic relevance determination effect in empirical Bayes but has a number of advantages. We reduce the number of parameters up to 280 times on LeNet architectures and up to 68 times on VGG-like networks with a negligible decrease of accuracy.

For self-driving cars and other smart transport to be successfully integrated in the real-world, the safety of passengers and pedestrians must be ensured. In the world of intelligent machines, perception answers the question: what is around me? This situational awareness is paramount for safe operation of autonomous vehicles in real-world environments. Scientists working in this field point to robotic perception as fundamental in equipping machines with a semantic understanding of the world, so that they can reliably identify objects and make informed predictions and actions. Michael Milford, Associate Professor at Queensland University of Technology (QUT), is a leading robotics researcher working to improve perception and more in autonomous vehicles, conducting his research at the intersection of robotics, neuroscience and computer vision.