Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. AMMs allow users to trade different types of crypto-tokens, without the need to find a counter-party. There are several implementations and models for AMMs, featuring a variety of sophisticated economic mechanisms. We present a theory of AMMs. The core of our theory is an abstract operational model of the interactions between users and AMMs, which can be concretised by instantiating the economic mechanisms. We exploit our theory to formally prove a set of fundamental properties of AMMs, characterizing both structural and economic aspects. We do this by abstracting from the actual economic mechanisms used in implementations and identifying sufficient conditions which ensure the relevant properties. Notably, we devise a general solution to the arbitrage problem, the main game-theoretic foundation behind the economic mechanisms of AMMs.
Applications of Reinforcement Learning (RL), in which agents learn to make a sequence of decisions despite lacking complete information about the latent states of the controlled system, that is, they act under partial observability of the states, are ubiquitous. Partially observable RL can be notoriously difficult -- well-known information-theoretic results show that learning partially observable Markov decision processes (POMDPs) requires an exponential number of samples in the worst case. Yet, this does not rule out the existence of large subclasses of POMDPs over which learning is tractable. In this paper we identify such a subclass, which we call weakly revealing POMDPs. This family rules out the pathological instances of POMDPs where observations are uninformative to a degree that makes learning hard. We prove that for weakly revealing POMDPs, a simple algorithm combining optimism and Maximum Likelihood Estimation (MLE) is sufficient to guarantee polynomial sample complexity. To the best of our knowledge, this is the first provably sample-efficient result for learning from interactions in overcomplete POMDPs, where the number of latent states can be larger than the number of observations.
Recruitment in large organisations often involves interviewing a large number of candidates. The process is resource intensive and complex. Therefore, it is important to carry it out efficiently and effectively. Planning the selection process consists of several problems, each of which maps to one or the other well-known computing problem. Research that looks at each of these problems in isolation is rich and mature. However, research that takes an integrated view of the problem is not common. In this paper, we take two of the most important aspects of the application processing problem, namely review/interview panel creation and interview scheduling. We have implemented our approach as a prototype system and have used it to automatically plan the interview process of a real-life data set. Our system provides a distinctly better plan than the existing practice, which is predominantly manual. We have explored various algorithmic options and have customised them to solve these panel creation and interview scheduling problems. We have evaluated these design options experimentally on a real data set and have presented our observations. Our prototype and experimental process and results may be a very good starting point for a full-fledged development project for automating application processing process.
As machine learning algorithms become increasingly integrated in crucial decision-making scenarios, such as healthcare, recruitment, and risk assessment, there have been increasing concerns about the privacy and fairness of such systems. Federated learning has been viewed as a promising solution for collaboratively training of machine learning models among multiple parties while maintaining the privacy of their local data. However, federated learning also poses new challenges in mitigating the potential bias against certain populations (e.g., demographic groups), as this typically requires centralized access to the sensitive information (e.g., race, gender) of each data point. Motivated by the importance and challenges of group fairness in federated learning, in this work, we propose FairFed, a novel algorithm to enhance group fairness via a fairness-aware aggregation method, which aims to provide fair model performance across different sensitive groups (e.g., racial, gender groups) while maintaining high utility. This formulation can further provide more flexibility in the customized local debiasing strategies for each client. We build our FairFed algorithm around the secure aggregation protocol of federated learning. When running federated training on widely investigated fairness datasets, we demonstrate that our proposed method outperforms the state-of-the-art fair federated learning frameworks under a high heterogeneous sensitive attribute distribution. We also investigate the performance of FairFed on naturally distributed real-life data collected from different geographical locations or departments within an organization.
Requirements engineering (RE) activities for Machine Learning (ML) are not well-established and researched in the literature. Many issues and challenges exist when specifying, designing, and developing ML-enabled systems. Adding more focus on RE for ML can help to develop more reliable ML-enabled systems. Based on insights collected from previous work and industrial experiences, we propose a catalogue of 45 concerns to be considered when specifying ML-enabled systems, covering five different perspectives we identified as relevant for such systems: objectives, user experience, infrastructure, model, and data. Examples of such concerns include the execution engine and telemetry for the infrastructure perspective, and explainability and reproducibility for the model perspective. We conducted a focus group session with eight software professionals with experience developing ML-enabled systems to validate the importance, quality and feasibility of using our catalogue. The feedback allowed us to improve the catalogue and confirmed its practical relevance. The main research contribution of this work consists in providing a validated set of concerns grouped into perspectives that can be used by requirements engineers to support the specification of ML-enabled systems.
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal likelihood (model evidence), which is computationally challenging, prohibiting its use in many high-dimensional Bayesian inverse problems. With Bayesian imaging applications in mind, in this work we present the proximal nested sampling methodology to objectively compare alternative Bayesian imaging models for applications that use images to inform decisions under uncertainty. The methodology is based on nested sampling, a Monte Carlo approach specialised for model comparison, and exploits proximal Markov chain Monte Carlo techniques to scale efficiently to large problems and to tackle models that are log-concave and not necessarily smooth (e.g., involving l_1 or total-variation priors). The proposed approach can be applied computationally to problems of dimension O(10^6) and beyond, making it suitable for high-dimensional inverse imaging problems. It is validated on large Gaussian models, for which the likelihood is available analytically, and subsequently illustrated on a range of imaging problems where it is used to analyse different choices of dictionary and measurement model.
Mechanism design is a central research branch in microeconomics. An effective mechanism can significantly improve performance and efficiency of social decisions under desired objectives, such as to maximize social welfare or to maximize revenue for agents. However, mechanism design is challenging for many common models including the public project problem model which we study in this thesis. A typical public project problem is a group of agents crowdfunding a public project (e.g., building a bridge). The mechanism will decide the payment and allocation for each agent (e.g., how much the agent pays, and whether the agent can use it) according to their valuations. The mechanism can be applied to various economic scenarios, including those related to cyber security. There are different constraints and optimized objectives for different public project scenarios (sub-problems), making it unrealistic to design a universal mechanism that fits all scenarios, and designing mechanisms for different settings manually is a taxing job. Therefore, we explore automated mechanism design (AMD) of public project problems under different constraints. In this thesis, we focus on the public project problem, which includes many sub-problems (excludable/non-excludable, divisible/indivisible, binary/non-binary). We study the classical public project model and extend this model to other related areas such as the zero-day exploit markets. For different sub-problems of the public project problem, we adopt different novel machine learning techniques to design optimal or near-optimal mechanisms via automated mechanism design. We evaluate our mechanisms by theoretical analysis or experimentally comparing our mechanisms against existing mechanisms. The experiments and theoretical results show that our mechanisms are better than state-of-the-art automated or manual mechanisms.
This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.
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.
Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges.