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We study the problem of approximating the eigenspectrum of a symmetric matrix $\mathbf A \in \mathbb{R}^{n \times n}$ with bounded entries (i.e., $\|\mathbf A\|_{\infty} \leq 1$). We present a simple sublinear time algorithm that approximates all eigenvalues of $\mathbf{A}$ up to additive error $\pm \epsilon n$ using those of a randomly sampled $\tilde {O}\left (\frac{\log^3 n}{\epsilon^3}\right ) \times \tilde O\left (\frac{\log^3 n}{\epsilon^3}\right )$ principal submatrix. Our result can be viewed as a concentration bound on the complete eigenspectrum of a random submatrix, significantly extending known bounds on just the singular values (the magnitudes of the eigenvalues). We give improved error bounds of $\pm \epsilon \sqrt{\text{nnz}(\mathbf{A})}$ and $\pm \epsilon \|\mathbf A\|_F$ when the rows of $\mathbf A$ can be sampled with probabilities proportional to their sparsities or their squared $\ell_2$ norms respectively. Here $\text{nnz}(\mathbf{A})$ is the number of non-zero entries in $\mathbf{A}$ and $\|\mathbf A\|_F$ is its Frobenius norm. Even for the strictly easier problems of approximating the singular values or testing the existence of large negative eigenvalues (Bakshi, Chepurko, and Jayaram, FOCS '20), our results are the first that take advantage of non-uniform sampling to give improved error bounds. From a technical perspective, our results require several new eigenvalue concentration and perturbation bounds for matrices with bounded entries. Our non-uniform sampling bounds require a new algorithmic approach, which judiciously zeroes out entries of a randomly sampled submatrix to reduce variance, before computing the eigenvalues of that submatrix as estimates for those of $\mathbf A$. We complement our theoretical results with numerical simulations, which demonstrate the effectiveness of our algorithms in practice.

If we want to train robots in simulation before deploying them in reality, it seems natural and almost self-evident to presume that reducing the sim2real gap involves creating simulators of increasing fidelity (since reality is what it is). We challenge this assumption and present a contrary hypothesis -- sim2real transfer of robots may be improved with lower (not higher) fidelity simulation. We conduct a systematic large-scale evaluation of this hypothesis on the problem of visual navigation -- in the real world, and on 2 different simulators (Habitat and iGibson) using 3 different robots (A1, AlienGo, Spot). Our results show that, contrary to expectation, adding fidelity does not help with learning; performance is poor due to slow simulation speed (preventing large-scale learning) and overfitting to inaccuracies in simulation physics. Instead, building simple models of the robot motion using real-world data can improve learning and generalization.

This paper presents the AWKWARD architecture for the development of hybrid agents in Multi-Agent Systems. AWKWARD agents can have their plans re-configured in real time to align with social role requirements under changing environmental and social circumstances. The proposed hybrid architecture makes use of Behaviour Oriented Design (BOD) to develop agents with reactive planning and of the well-established OperA framework to provide organisational, social, and interaction definitions in order to validate and adjust agents' behaviours. Together, OperA and BOD can achieve real-time adjustment of agent plans for evolving social roles, while providing the additional benefit of transparency into the interactions that drive this behavioural change in individual agents. We present this architecture to motivate the bridging between traditional symbolic- and behaviour-based AI communities, where such combined solutions can help MAS researchers in their pursuit of building stronger, more robust intelligent agent teams. We use DOTA2, a game where success is heavily dependent on social interactions, as a medium to demonstrate a sample implementation of our proposed hybrid architecture.

Detecting and mitigating harmful biases in modern language models are widely recognized as crucial, open problems. In this paper, we take a step back and investigate how language models come to be biased in the first place. We use a relatively small language model, using the LSTM architecture trained on an English Wikipedia corpus. With full access to the data and to the model parameters as they change during every step while training, we can map in detail how the representation of gender develops, what patterns in the dataset drive this, and how the model's internal state relates to the bias in a downstream task (semantic textual similarity). We find that the representation of gender is dynamic and identify different phases during training. Furthermore, we show that gender information is represented increasingly locally in the input embeddings of the model and that, as a consequence, debiasing these can be effective in reducing the downstream bias. Monitoring the training dynamics, allows us to detect an asymmetry in how the female and male gender are represented in the input embeddings. This is important, as it may cause naive mitigation strategies to introduce new undesirable biases. We discuss the relevance of the findings for mitigation strategies more generally and the prospects of generalizing our methods to larger language models, the Transformer architecture, other languages and other undesirable biases.

Mechanistic simulators are an indispensable tool for epidemiology to explore the behavior of complex, dynamic infections under varying conditions and navigate uncertain environments. ODE-based models are the dominant paradigm that enable fast simulations and are tractable to gradient-based optimization, but make simplifying assumptions about population homogeneity. Agent-based models (ABMs) are an increasingly popular alternative paradigm that can represent the heterogeneity of contact interactions with granular detail and agency of individual behavior. However, conventional ABM frameworks are not differentiable and present challenges in scalability; due to which it is non-trivial to connect them to auxiliary data sources easily. In this paper we introduce GradABM which is a new scalable, fast and differentiable design for ABMs. GradABM runs simulations in few seconds on commodity hardware and enables fast forward and differentiable inverse simulations. This makes it amenable to be merged with deep neural networks and seamlessly integrate heterogeneous data sources to help with calibration, forecasting and policy evaluation. We demonstrate the efficacy of GradABM via extensive experiments with real COVID-19 and influenza datasets. We are optimistic this work will bring ABM and AI communities closer together.

In our time cybersecurity has grown to be a topic of massive proportion at the national and enterprise levels. Our thesis is that the economic perspective and investment decision-making are vital factors in determining the outcome of the struggle. To build our economic framework, we borrow from the pioneering work of Gordon and Loeb in which the Defender optimally trades-off investments for lower likelihood of its system breach. Our two-sided model additionally has an Attacker, assumed to be rational and also guided by economic considerations in its decision-making, to which the Defender responds. Our model is a simplified adaptation of a model proposed during the Cold War for weapons deployment in the US. Our model may also be viewed as a Stackelberg game and, from an analytic perspective, as a Max-Min problem, the analysis of which is known to have to contend with discontinuous behavior. The complexity of our simple model is rooted in its inherent nonlinearity and, more consequentially, non-convexity of the objective function in the optimization. The possibilities of the Attacker's actions add substantially to the risk to the Defender, and the Defender's rational, risk-neutral optimal investments in general substantially exceed the optimal investments predicted by the one-sided Gordon-Loeb model. We obtain a succinct set of three decision types that categorize all of the Defender's optimal investment decisions. Also, the Defender's optimal decisions exhibit discontinuous behavior as the initial vulnerability of its system is varied. The analysis is supplemented by extensive numerical illustrations. The results from our model open several major avenues for future work.

This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. Our proposed estimators show, in certain settings, mean squared error improvements compared to both canonical and state-of-the-art estimators. We show that recent research on distributionally robust prediction methods has connections to well-studied estimators from econometrics. This connection leads us to prove that general K-class estimators possess distributional robustness properties. We, furthermore, propose a general framework for distributional robustness with respect to intervention-induced distributions. In this framework, we derive sufficient conditions for the identifiability of distributionally robust prediction methods and present impossibility results that show the necessity of several of these conditions. We present a new structure learning method applicable in additive noise models with directed trees as causal graphs. We prove consistency in a vanishing identifiability setup and provide a method for testing substructure hypotheses with asymptotic family-wise error control that remains valid post-selection. Finally, we present heuristic ideas for learning summary graphs of nonlinear time-series models.

Bid optimization for online advertising from single advertiser's perspective has been thoroughly investigated in both academic research and industrial practice. However, existing work typically assume competitors do not change their bids, i.e., the wining price is fixed, leading to poor performance of the derived solution. Although a few studies use multi-agent reinforcement learning to set up a cooperative game, they still suffer the following drawbacks: (1) They fail to avoid collusion solutions where all the advertisers involved in an auction collude to bid an extremely low price on purpose. (2) Previous works cannot well handle the underlying complex bidding environment, leading to poor model convergence. This problem could be amplified when handling multiple objectives of advertisers which are practical demands but not considered by previous work. In this paper, we propose a novel multi-objective cooperative bid optimization formulation called Multi-Agent Cooperative bidding Games (MACG). MACG sets up a carefully designed multi-objective optimization framework where different objectives of advertisers are incorporated. A global objective to maximize the overall profit of all advertisements is added in order to encourage better cooperation and also to protect self-bidding advertisers. To avoid collusion, we also introduce an extra platform revenue constraint. We analyze the optimal functional form of the bidding formula theoretically and design a policy network accordingly to generate auction-level bids. Then we design an efficient multi-agent evolutionary strategy for model optimization. Offline experiments and online A/B tests conducted on the Taobao platform indicate both single advertiser's objective and global profit have been significantly improved compared to state-of-art methods.

Recent years have witnessed significant advances in technologies and services in modern network applications, including smart grid management, wireless communication, cybersecurity as well as multi-agent autonomous systems. Considering the heterogeneous nature of networked entities, emerging network applications call for game-theoretic models and learning-based approaches in order to create distributed network intelligence that responds to uncertainties and disruptions in a dynamic or an adversarial environment. This paper articulates the confluence of networks, games and learning, which establishes a theoretical underpinning for understanding multi-agent decision-making over networks. We provide an selective overview of game-theoretic learning algorithms within the framework of stochastic approximation theory, and associated applications in some representative contexts of modern network systems, such as the next generation wireless communication networks, the smart grid and distributed machine learning. In addition to existing research works on game-theoretic learning over networks, we highlight several new angles and research endeavors on learning in games that are related to recent developments in artificial intelligence. Some of the new angles extrapolate from our own research interests. The overall objective of the paper is to provide the reader a clear picture of the strengths and challenges of adopting game-theoretic learning methods within the context of network systems, and further to identify fruitful future research directions on both theoretical and applied studies.

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.