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Deep learning approaches have shown promising results in solving routing problems. However, there is still a substantial gap in solution quality between machine learning and operations research algorithms. Recently, another line of research has been introduced that fuses the strengths of machine learning and operational research algorithms. In particular, search perturbation operators have been used to improve the solution. Nevertheless, using the perturbation may not guarantee a quality solution. This paper presents "Learning to Guide Local Search" (L2GLS), a learning-based approach for routing problems that uses a penalty term and reinforcement learning to adaptively adjust search efforts. L2GLS combines local search (LS) operators' strengths with penalty terms to escape local optimals. Routing problems have many practical applications, often presetting larger instances that are still challenging for many existing algorithms introduced in the learning to optimise field. We show that L2GLS achieves the new state-of-the-art results on larger TSP and CVRP over other machine learning methods.

Machine learning (ML) provides us with numerous opportunities, allowing ML systems to adapt to new situations and contexts. At the same time, this adaptability raises uncertainties concerning the run-time product quality or dependability, such as reliability and security, of these systems. Systems can be tested and monitored, but this does not provide protection against faults and failures in adapted ML systems themselves. We studied software designs that aim at introducing fault tolerance in ML systems so that possible problems in ML components of the systems can be avoided. The research was conducted as a case study, and its data was collected through five semi-structured interviews with experienced software architects. We present a conceptualisation of the misbehaviour of ML systems, the perceived role of fault tolerance, and the designs used. Common patterns to incorporating ML components in design in a fault tolerant fashion have started to emerge. ML models are, for example, guarded by monitoring the inputs and their distribution, and enforcing business rules on acceptable outputs. Multiple, specialised ML models are used to adapt to the variations and changes in the surrounding world, and simpler fall-over techniques like default outputs are put in place to have systems up and running in the face of problems. However, the general role of these patterns is not widely acknowledged. This is mainly due to the relative immaturity of using ML as part of a complete software system: the field still lacks established frameworks and practices beyond training to implement, operate, and maintain the software that utilises ML. ML software engineering needs further analysis and development on all fronts.

Reconfigurable Intelligent Surfaces (RISs), comprising large numbers of low-cost and passive metamaterials with tunable reflection properties, have been recently proposed as an enabler for programmable radio propagation environments. However, the role of the channel conditions near the RISs on their optimizability has not been analyzed adequately. In this paper, we present an asymptotic closed-form expression for the mutual information of a multi-antenna transmitter-receiver pair in the presence of multiple RISs, in the large-antenna limit, using the random matrix and replica theories. Under mild assumptions, asymptotic expressions for the eigenvalues and the eigenvectors of the channel covariance matrices are derived. We find that, when the channel close to an RIS is correlated, for instance due to small angle spread, the communication link benefits significantly from the RIS optimization, resulting in gains that are surprisingly higher than the nearly uncorrelated case. Furthermore, when the desired reflection from the RIS departs significantly from geometrical optics, the surface can be optimized to provide robust communication links. Building on the properties of the eigenvectors of the covariance matrices, we are able to find the optimal response of the RISs in closed form, bypassing the need for brute-force optimization.

We consider the learning task of prediction of formation of core stable coalition structure in hedonic games based on agents' noisy preferences. We have considered two cases: complete information (noisy preferences of all the agents are entirely known) and partial information (noisy preferences over some coalitions are only known). We introduce a noise model that probabilistically scales the valuations of coalitions. The performance metric is the probability of our prediction conditioned on all or few noisy preferences of the agents be correct. The nature of our results is that this prediction probability is relatively low, including being zero, and rarely it is one. In the complete information two-agent model, in which each agent `retains' or `inflates' the values of its coalitions, we identify the expressions of the prediction probabilities in terms of the noise probability. We identify the interval of the noise probability such that the prediction probability is at least a user-given threshold. It turned out that, for some noisy games, the noise probability interval does not exist for a threshold as low as 0.1481, thus demonstrating that the prediction probabilities are generally low even in this model. In the partial information setup, we consider $n$ agent games with $l$ support of noise values, and such noisy preferences are available for some coalitions only. We obtain the bounds on the prediction probability of a partition to be $\epsilon$-PAC stable in the noise-free game in the cases when the realized noisy game has or hasn't $\epsilon$-PAC stable outcome.

This paper proposes a novel scalable reinforcement learning approach for simultaneous routing and spectrum access in wireless ad-hoc networks. In most previous works on reinforcement learning for network optimization, the network topology is assumed to be fixed, and a different agent is trained for each transmission node -- this limits scalability and generalizability. Further, routing and spectrum access are typically treated as separate tasks. Moreover, the optimization objective is usually a cumulative metric along the route, e.g., number of hops or delay. In this paper, we account for the physical-layer signal-to-interference-plus-noise ratio (SINR) in a wireless network and further show that bottleneck objective such as the minimum SINR along the route can also be optimized effectively using reinforcement learning. Specifically, we propose a scalable approach in which a single agent is associated with each flow and makes routing and spectrum access decisions as it moves along the frontier nodes. The agent is trained according to the physical-layer characteristics of the environment using a novel rewarding scheme based on the Monte Carlo estimation of the future bottleneck SINR. It learns to avoid interference by intelligently making joint routing and spectrum allocation decisions based on the geographical location information of the neighbouring nodes.

The difficulty in specifying rewards for many real-world problems has led to an increased focus on learning rewards from human feedback, such as demonstrations. However, there are often many different reward functions that explain the human feedback, leaving agents with uncertainty over what the true reward function is. While most policy optimization approaches handle this uncertainty by optimizing for expected performance, many applications demand risk-averse behavior. We derive a novel policy gradient-style robust optimization approach, PG-BROIL, that optimizes a soft-robust objective that balances expected performance and risk. To the best of our knowledge, PG-BROIL is the first policy optimization algorithm robust to a distribution of reward hypotheses which can scale to continuous MDPs. Results suggest that PG-BROIL can produce a family of behaviors ranging from risk-neutral to risk-averse and outperforms state-of-the-art imitation learning algorithms when learning from ambiguous demonstrations by hedging against uncertainty, rather than seeking to uniquely identify the demonstrator's reward function.

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.

When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.

Personalized recommendation systems (RS) are extensively used in many services. Many of these are based on learning algorithms where the RS uses the recommendation history and the user response to learn an optimal strategy. Further, these algorithms are based on the assumption that the user interests are rigid. Specifically, they do not account for the effect of learning strategy on the evolution of the user interests. In this paper we develop influence models for a learning algorithm that is used to optimally recommend websites to web users. We adapt the model of \cite{Ioannidis10} to include an item-dependent reward to the RS from the suggestions that are accepted by the user. For this we first develop a static optimisation scheme when all the parameters are known. Next we develop a stochastic approximation based learning scheme for the RS to learn the optimal strategy when the user profiles are not known. Finally, we describe several user-influence models for the learning algorithm and analyze their effect on the steady user interests and on the steady state optimal strategy as compared to that when the users are not influenced.

Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): finding mappings of request graphs (describing the workloads) onto a substrate graph (describing the physical infrastructure). In the offline setting, the two natural objectives are profit maximization, i.e., embedding a maximal number of request graphs subject to the resource constraints, and cost minimization, i.e., embedding all requests at minimal overall cost. The VNEP can be seen as a generalization of classic routing and call admission problems, in which requests are arbitrary graphs whose communication endpoints are not fixed. Due to its applications, the problem has been studied intensively in the networking community. However, the underlying algorithmic problem is hardly understood. This paper presents the first fixed-parameter tractable approximation algorithms for the VNEP. Our algorithms are based on randomized rounding. Due to the flexible mapping options and the arbitrary request graph topologies, we show that a novel linear program formulation is required. Only using this novel formulation the computation of convex combinations of valid mappings is enabled, as the formulation needs to account for the structure of the request graphs. Accordingly, to capture the structure of request graphs, we introduce the graph-theoretic notion of extraction orders and extraction width and show that our algorithms have exponential runtime in the request graphs' maximal width. Hence, for request graphs of fixed extraction width, we obtain the first polynomial-time approximations. Studying the new notion of extraction orders we show that (i) computing extraction orders of minimal width is NP-hard and (ii) that computing decomposable LP solutions is in general NP-hard, even when restricting request graphs to planar ones.