Truthful approximations to range voting

We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare maximization in this setting. With m being the number of alternatives, we exhibit a randomized truthful-in-expectation ordinal mechanism implementing an outcome whose expected social welfare is at least an Omega(m^{-3/4}) fraction of the social welfare of the socially optimal alternative. On the other hand, we show that for sufficiently many agents and any truthful-in-expectation ordinal mechanism, there is a valuation profile where the mechanism achieves at most an O(m^{-{2/3}) fraction of the optimal social welfare in expectation. We get tighter bounds for the natural special case of m = 3, and in that case furthermore obtain separation results concerning the approximation ratios achievable by natural restricted classes of truthful-in-expectation mechanisms. In particular, we show that for m = 3 and a sufficiently large number of agents, the best mechanism that is ordinal as well as mixed-unilateral has an approximation ratio between 0.610 and 0.611, the best ordinal mechanism has an approximation ratio between 0.616 and 0.641, while the best mixed-unilateral mechanism has an approximation ratio bigger than 0.660. In particular, the best mixed-unilateral non-ordinal (i.e., cardinal) mechanism strictly outperforms all ordinal ones, even the non-mixed-unilateral ordinal ones

Planning with learned ignorance-aware models

One of the goals of artificial intelligence research is to create decision-makers (i.e., agents) that improve from experience (i.e., data), collected through interaction with an environment. Models of the environment (i.e., world models) are an explicit way that agents use to represent their knowledge, enabling them to make counterfactual predictions and plans without requiring additional environment interactions. Although agents that plan with a perfect model of the environment have led to impressive demonstrations, e.g., super- human performance in board games, they are limited to problems their designer can specify a perfect model. Therefore, learning models from experience holds the promise of going beyond the scope of their designers’ reach, giving rise to a self-improving vicious circle of (i) learning a model from the past experience; (ii) planning with the learned model; and (iii) interacting with the environment, collecting new experiences. Ideally, learned models should generalise to situations beyond their training regime. Nonetheless, this is ambitious and often unrealistic when finite data is used for learning the models, leading to generally imperfect models, with which naive planning could be catastrophic in novel, out-of-training distribution situations. A more pragmatic goal is to have agents that are aware of and quantify their lack of knowledge (i.e., ignorance or epistemic uncertainty). In this thesis, we motivate and demonstrate the effectiveness of and propose novel ignorance-aware agents that plan with learned models. Naively applying powerful planning algorithms to learned models can render negative results, when the planning algorithm exploits the model imperfections in out-of-training distribution situations. This phenomenon is often termed overoptimisation and can be addressed by optimising ignorance-augmented objectives, called knowledge equivalents. We verify the validity of our ideas and methods in a number of problem settings, including learning from (i) expert demonstrations (imitation learning, §3); (ii) sub-optimal demonstrations (social learning, §4); and (iii) interacting with an environment with rewards (reinforcement learning, §5). Our empirical evidence is based on simulated autonomous driving environments, continuous control and video games from pixels and didactic small-scale grid-worlds. Throughout the thesis, we use neural networks to parameterise the (learnable) models and either use existing scalable approximate ignorance quantification deep learning methods, such as ensembles, or introduce novel planning-specific ways to quantify the agents’ ignorance. The main chapters of this thesis are based on publications (Filos et al., 2020, 2021, 2022)

Facility location with double-peaked preference

We study the problem of locating a single facility on a real line based on the reports of self-interested agents, when agents have double-peaked preferences, with the peaks being on opposite sides of their locations. We observe that double-peaked preferences capture real-life scenarios and thus complement the well-studied notion of single-peaked preferences. We mainly focus on the case where peaks are equidistant from the agents' locations and discuss how our results extend to more general settings. We show that most of the results for single-peaked preferences do not directly apply to this setting; this makes the problem essentially more challenging. As our main contribution, we present a simple truthful-in-expectation mechanism that achieves an approximation ratio of 1+b/c for both the social and the maximum cost, where b is the distance of the agent from the peak and c is the minimum cost of an agent. For the latter case, we provide a 3/2 lower bound on the approximation ratio of any truthful-in-expectation mechanism. We also study deterministic mechanisms under some natural conditions, proving lower bounds and approximation guarantees. We prove that among a large class of reasonable mechanisms, there is no deterministic mechanism that outperforms our truthful-in-expectation mechanism

Towards Explainable and Trustworthy AI for Decision Support in Medicine: An Overview of Methods and Good Practices

Artificial Intelligence (AI) is defined as intelligence exhibited by machines, such as electronic computers. It can involve reasoning, problem solving, learning and knowledge representation, which are mostly in focus in the medical domain. Other forms of intelligence, including autonomous behavior, are also parts of AI. Data driven methods for decision support have been employed in the medical domain for some time. Machine learning (ML) is used for a wide range of complex tasks across many sectors of the industry. However, a broader spectrum of AI, including deep learning (DL) as well as autonomous agents, have been recently gaining more focus and have risen expectation for solving numerous problems in the medical domain. A barrier towards AI adoption, or rather a concern, is trust in AI, which is often hindered by issues like lack of understanding of a black-box model function, or lack of credibility related to reporting of results. Explainability and interpretability are prerequisites for the development of AI-based systems that are lawful, ethical and robust. In this respect, this paper presents an overview of concepts, best practices, and success stories, and opens the discussion for multidisciplinary work towards establishing trustworthy AI

Consensus-Halving: Does It Ever Get Easier?

In the $\varepsilon$-Consensus-Halving problem, a fundamental problem in fair division, there are $n$ agents with valuations over the interval $[0,1]$, and the goal is to divide the interval into pieces and assign a label "$+$" or "$-$" to each piece, such that every agent values the total amount of "$+$" and the total amount of "$-$" almost equally. The problem was recently proven by Filos-Ratsikas and Goldberg [2019] to be the first "natural" complete problem for the computational class PPA, answering a decade-old open question. In this paper, we examine the extent to which the problem becomes easy to solve, if one restricts the class of valuation functions. To this end, we provide the following contributions. First, we obtain a strengthening of the PPA-hardness result of [Filos-Ratsikas and Goldberg, 2019], to the case when agents have piecewise uniform valuations with only two blocks. We obtain this result via a new reduction, which is in fact conceptually much simpler than the corresponding one in [Filos-Ratsikas and Goldberg, 2019]. Then, we consider the case of single-block (uniform) valuations and provide a parameterized polynomial time algorithm for solving $\varepsilon$-Consensus-Halving for any $\varepsilon$, as well as a polynomial-time algorithm for $\varepsilon=1/2$; these are the first algorithmic results for the problem. Finally, an important application of our new techniques is the first hardness result for a generalization of Consensus-Halving, the Consensus-$1/k$-Division problem. In particular, we prove that $\varepsilon$-Consensus-$1/3$-Division is PPAD-hard