arXiv subjects

Joe Halpern

Publications and source records attributed to Joe Halpern.

4 recordsLinked to original sources

arXiv2024

Fair Interest Rates Are Impossible for Lending Pools: Results from Options Pricing

Cryptocurrency lending pools are services that allow lenders to pool together assets in one cryptocurrency and loan it out to borrowers who provide collateral worth more (than the loan) in a separate cryptocurrency. Borrowers can repay their loans to reclaim their collateral unless their loan was liquidated, which happens when the value of the collateral dips significantly. Interest rates for these pools are currently set via supply and demand heuristics, which have several downsides, including inefficiency, inflexibility, and being vulnerable to manipulation. Here, we reduce lending pools to options, and then use ideas from options pricing to search for fair interest rates for lending pools. In a simplified model where the loans have a fixed duration and can only be repaid at the end of the term, we obtain analytical pricing results. We then consider a more realistic model, where loans can be repaid dynamically and without expiry. Our main theoretical contribution is to show that fair interest rates do not exist in this setting. We then show that impossibility results generalize even to models of lending pools which have no obvious reduction to options. To address these negative results, we introduce a model of lending pools with fixed fees, and model the ability of borrowers to top-up their loans to reduce the risk of liquidation. As a proof of concept, we use simulations to show how our model's predicted interest rates compare to interest rates in practice.

cs.CE↗

arXiv2024

Games with Payments between Learning Agents

In repeated games, such as auctions, players rely on autonomous learning agents to choose their actions. We study settings in which players have their agents make monetary transfers to other agents during play at their own expense, in order to influence learning dynamics in their favor. Our goal is to understand when players have incentives to use such payments, how payments between agents affect learning outcomes, and what the resulting implications are for welfare and its distribution. We propose a simple game-theoretic model to capture the incentive structure of such scenarios. We find that, quite generally, abstaining from payments is not robust to strategic deviations by users of learning agents: self-interested players benefit from having their agents make payments to other learners. In a broad class of games, such endogenous payments between learning agents lead to higher welfare for all players. In first- and second-price auctions, equilibria of the induced "payment-policy game" lead to highly collusive learning outcomes, with low or vanishing revenue for the auctioneer. These results highlight a fundamental challenge for mechanism design, as well as for regulatory policies, in environments where learning agents may interact in the digital ecosystem beyond a mechanism's boundaries.

cs.GT↗

arXiv2024

Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems

Ensuring that AI systems reliably and robustly avoid harmful or dangerous behaviours is a crucial challenge, especially for AI systems with a high degree of autonomy and general intelligence, or systems used in safety-critical contexts. In this paper, we will introduce and define a family of approaches to AI safety, which we will refer to as guaranteed safe (GS) AI. The core feature of these approaches is that they aim to produce AI systems which are equipped with high-assurance quantitative safety guarantees. This is achieved by the interplay of three core components: a world model (which provides a mathematical description of how the AI system affects the outside world), a safety specification (which is a mathematical description of what effects are acceptable), and a verifier (which provides an auditable proof certificate that the AI satisfies the safety specification relative to the world model). We outline a number of approaches for creating each of these three core components, describe the main technical challenges, and suggest a number of potential solutions to them. We also argue for the necessity of this approach to AI safety, and for the inadequacy of the main alternative approaches.

cs.AI↗

arXiv2023

Chunking Tasks for Present-Biased Agents

Everyone puts things off sometimes. How can we combat this tendency to procrastinate? A well-known technique used by instructors is to break up a large project into more manageable chunks. But how should this be done best? Here we study the process of chunking using the graph-theoretic model of present bias introduced by Kleinberg and Oren (2014). We first analyze how to optimally chunk single edges within a task graph, given a limited number of chunks. We show that for edges on the shortest path, the optimal chunking makes initial chunks easy and later chunks progressively harder. For edges not on the shortest path, optimal chunking is significantly more complex, but we provide an efficient algorithm that chunks the edge optimally. We then use our optimal edge-chunking algorithm to optimally chunk task graphs. We show that with a linear number of chunks on each edge, the biased agent's cost can be exponentially lowered, to within a constant factor of the true cheapest path. Finally, we extend our model to the case where a task designer must chunk a graph for multiple types of agents simultaneously. The problem grows significantly more complex with even two types of agents, but we provide optimal graph chunking algorithms for two types. Our work highlights the efficacy of chunking as a means to combat present bias.

cs.GT↗