Toby Walsh

We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility result that no strategy proof mechanism can bound the approximation ratio of the optimal Gini index of utilities for one or more facilities. We propose instead computing approximation ratios of the complemented Gini index of utilities, and consider how well both deterministic and randomized mechanisms approximate this. In addition, as Nash welfare is often put forwards as an equitable compromise between egalitarain and utilitarian outcomes, we consider how well mechanisms approximate the Nash welfare.

We study mechanisms for the facility location problem augmented with predictions of the optimal facility location. We demonstrate that an egalitarian viewpoint which considers both the maximum distance of any agent from the facility and the minimum utility of any agent provides important new insights compared to a viewpoint that just considers the maximum distance. As in previous studies, we consider performance in terms of consistency (worst case when predictions are accurate) and robustness (worst case irrespective of the accuracy of predictions). By considering how mechanisms with predictions can perform poorly, we design new mechanisms that are more robust. Indeed, by adjusting parameters, we demonstrate how to trade robustness for consistency. We go beyond the single facility problem by designing novel strategy proof mechanisms for locating two facilities with bounded consistency and robustness that use two predictions for where to locate the two facilities.

We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility result that no strategy proof mechanism can bound the approximation ratio of the optimal Gini index of utilities for one or more facilities. We propose instead computing approximation ratios of the complemented Gini index of utilities, and consider how well both deterministic and randomized mechanisms approximate this. In addition, as Nash welfare is often put forwards as an equitable compromise between egalitarian and utilitarian outcomes, we consider how well mechanisms approximate the Nash welfare.

We identify strategy proof mechanisms for facility location that simultaneously approximate well both the maximum distance from the nearest facility and the minimum utility of any agent. Somewhat surprisingly, while the deterministic MEDIAN and the randomized ENDORAV mechanisms perform optimally with respect to approximating the maximum distance, neither perform optimally with respect to approximating the minimum utility. With deterministic mechanisms for locating a single facility, we prove that the MIDORNEAREST mechanism is optimal with respect to approximating both the maximum distance and the minimum utility. By comparison, the MEDIAN mechanism has an unbounded approximation ratio for approximating the minimum utility. With randomized mechanisms for locating a single facility, we construct the first mechanism that is optimal with respect to approximating the minimum utility. For deterministic and randomized mechanisms locating two or more facilities, we identify strategy proof mechanisms that are within a constant factor of optimal with respect to both objectives.

Randomized mechanisms can have good normative properties compared to their deterministic counter-parts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to de-randomize such mechanisms by having agents play a game instead of tossing a coin. The game is designed so agents play randomly, and this play injects “randomness” into the mechanism. Surprisingly this de-randomization retains many of the good normative properties of the original randomized mechanism but gives a mechanism that is deterministic and easy, for instance, to audit. We consider three general purpose methods to de-randomize mechanisms, and apply these to six different domains: voting, facility location, task allocation, school choice, peer selection, and resource allocation. We propose a number of novel de-randomized mechanisms for these six domains with good normative properties (such as equilibria in which agents sincerely report preferences over the original problem). In one domain, we additionally show that a new and desirable normative property emerges as a result of de-randomization.property emerges as a result of de-randomization.

ChatGPT burst into people's lives at the end of 2022, heralding the arrival of large language models in particular, and generative AI in general. How best to see this moment in the development of AI. What is generative AI actually good for? And what are its limitations? And how might we tackle them? In this talk, I'll explore how to understand recent breakthroughs in AI, and discuss what might come next.

This chapter explores the ways in which organisational readiness and scientific advances in Artificial Intelligence have been affecting the demand for skills and their training in Australia and other nations leading in the promotion, use, or development of AI. The consensus appears that having adequate number of qualified data scientists and machine learning experts is critical for meeting the challenges ahead. The chapter asks what this may mean for Australia’s education and training system, what needs to be taught and learned, and whether technical skills are all that matter.

We consider the problem of locating a facility to serve a set of agents located along a line. The Nash welfare objective function, defined as the product of the agents' utilities, is known to provide a compromise between fairness and efficiency in resource allocation problems. We apply this welfare notion to the facility location problem, converting individual costs to utilities and analyzing the facility placement that maximizes the Nash welfare. We give a polynomial-time approximation algorithm to compute this facility location, and prove results suggesting that it achieves a good balance of fairness and efficiency. Finally, we take a mechanism design perspective and propose a strategy-proof mechanism with a bounded approximation ratio for Nash welfare.