Can CDT rationalise the ex ante optimal policy via modified anthropics?

In Newcomb's problem, causal decision theory (CDT) recommends two-boxing and thus comes apart from evidential decision theory (EDT) and ex ante policy optimisation (which prescribe one-boxing). However, in Newcomb's problem, you should perhaps believe that with some probability you are in a simulation run by the predictor to determine whether to put a million dollars into the opaque box. If so, then causal decision theory might recommend one-boxing in order to cause the predictor to fill the opaque box. In this paper, we study generalisations of this approach. That is, we consider general Newcomblike problems and try to form reasonable self-locating beliefs under which CDT's recommendations align with an EDT-like notion of ex ante policy optimisation. We consider approaches in which we model the world as running simulations of the agent, and an approach not based on such models (which we call 'Generalised Generalised Thirding', or GGT). For each approach, we characterise the resulting CDT policies, and prove that under certain conditions, these include the ex ante optimal policies.

Game Theory with Simulation in the Presence of Unpredictable Randomisation

AI agents will be predictable in certain ways that traditional agents are not. Where and how can we leverage this predictability in order to improve social welfare? We study this question in a game-theoretic setting where one agent can pay a fixed cost to simulate the other in order to learn its mixed strategy. As a negative result, we prove that, in contrast to prior work on pure-strategy simulation, enabling mixed-strategy simulation may no longer lead to improved outcomes for both players in all so-called "generalised trust games". In fact, mixed-strategy simulation does not help in any game where the simulatee's action can depend on that of the simulator. We also show that, in general, deciding whether simulation introduces Pareto-improving Nash equilibria in a given game is NP-hard. As positive results, we establish that mixed-strategy simulation can improve social welfare if the simulator has the option to scale their level of trust, if the players face challenges with both trust and coordination, or if maintaining some level of privacy is essential for enabling cooperation.

On The Stability of Moral Preferences: A Problem with Computational Elicitation Methods

Preference elicitation frameworks feature heavily in the research on participatory ethical AI tools and provide a viable mechanism to enquire and incorporate the moral values of various stakeholders. As part of the elicitation process, surveys about moral preferences, opinions, and judgments are typically administered only once to each participant. This methodological practice is reasonable if participants' responses are stable over time such that, all other relevant factors being held constant, their responses today will be the same as their responses to the same questions at a later time. However, we do not know how often that is the case. It is possible that participants' true moral preferences change, are subject to temporary moods or whims, or are influenced by environmental factors we don't track. If participants' moral responses are unstable in such ways, it would raise important methodological and theoretical issues for how participants' true moral preferences, opinions, and judgments can be ascertained. We address this possibility here by asking the same survey participants the same moral questions about which patient should receive a kidney when only one is available ten times in ten different sessions over two weeks, varying only presentation order across sessions. We measured how often participants gave different responses to simple (Study One) and more complicated (Study Two) repeated scenarios. On average, the fraction of times participants changed their responses to controversial scenarios was around 10-18% across studies, and this instability is observed to have positive associations with response time and decision-making difficulty. We discuss the implications of these results for the efficacy of moral preference elicitation, highlighting the role of response instability in causing value misalignment between stakeholders and AI tools trained on their moral judgments.

On the Pros and Cons of Active Learning for Moral Preference Elicitation

Computational preference elicitation methods are tools used to learn people's preferences quantitatively in a given context. Recent works on preference elicitation advocate for active learning as an efficient method to iteratively construct queries (framed as comparisons between context-specific cases) that are likely to be most informative about an agent's underlying preferences. In this work, we argue that the use of active learning for moral preference elicitation relies on certain assumptions about the underlying moral preferences, which can be violated in practice. Specifically, we highlight the following common assumptions (a) preferences are stable over time and not sensitive to the sequence of presented queries, (b) the appropriate hypothesis class is chosen to model moral preferences, and (c) noise in the agent's responses is limited. While these assumptions can be appropriate for preference elicitation in certain domains, prior research on moral psychology suggests they may not be valid for moral judgments. Through a synthetic simulation of preferences that violate the above assumptions, we observe that active learning can have similar or worse performance than a basic random query selection method in certain settings. Yet, simulation results also demonstrate that active learning can still be viable if the degree of instability or noise is relatively small and when the agent's preferences can be approximately represented with the hypothesis class used for learning. Our study highlights the nuances associated with effective moral preference elicitation in practice and advocates for the cautious use of active learning as a methodology to learn moral preferences.

Why should we ever automate moral decision making?

While people generally trust AI to make decisions in various aspects of their lives, concerns arise when AI is involved in decisions with significant moral implications. The absence of a precise mathematical framework for moral reasoning intensifies these concerns, as ethics often defies simplistic mathematical models. Unlike fields such as logical reasoning, reasoning under uncertainty, and strategic decision-making, which have well-defined mathematical frameworks, moral reasoning lacks a broadly accepted framework. This absence raises questions about the confidence we can place in AI's moral decision-making capabilities. The environments in which AI systems are typically trained today seem insufficiently rich for such a system to learn ethics from scratch, and even if we had an appropriate environment, it is unclear how we might bring about such learning. An alternative approach involves AI learning from human moral decisions. This learning process can involve aggregating curated human judgments or demonstrations in specific domains, or leveraging a foundation model fed with a wide range of data. Still, concerns persist, given the imperfections in human moral decision making. Given this, why should we ever automate moral decision making -- is it not better to leave all moral decision making to humans? This paper lays out a number of reasons why we should expect AI systems to engage in decisions with a moral component, with brief discussions of the associated risks.

Imperfect-Recall Games: Equilibrium Concepts and Their Complexity

We investigate optimal decision making under imperfect recall, that is, when an agent forgets information it once held before. An example is the absentminded driver game, as well as team games in which the members have limited communication capabilities. In the framework of extensive-form games with imperfect recall, we analyze the computational complexities of finding equilibria in multiplayer settings across three different solution concepts: Nash, multiselves based on evidential decision theory (EDT), and multiselves based on causal decision theory (CDT). We are interested in both exact and approximate solution computation. As special cases, we consider (1) single-player games, (2) two-player zero-sum games and relationships to maximin values, and (3) games without exogenous stochasticity (chance nodes). We relate these problems to the complexity classes P, PPAD, PLS, $\Sigma_2^P$ , $\exists$R, and $\exists \forall$R.

Social Choice for AI Alignment: Dealing with Diverse Human Feedback

Foundation models such as GPT-4 are fine-tuned to avoid unsafe or otherwise problematic behavior, so that, for example, they refuse to comply with requests for help with committing crimes or with producing racist text. One approach to fine-tuning, called reinforcement learning from human feedback, learns from humans' expressed preferences over multiple outputs. Another approach is constitutional AI, in which the input from humans is a list of high-level principles. But how do we deal with potentially diverging input from humans? How can we aggregate the input into consistent data about ''collective'' preferences or otherwise use it to make collective choices about model behavior? In this paper, we argue that the field of social choice is well positioned to address these questions, and we discuss ways forward for this agenda, drawing on discussions in a recent workshop on Social Choice for AI Ethics and Safety held in Berkeley, CA, USA in December 2023.

Recursive Joint Simulation in Games

Game-theoretic dynamics between AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to accurately simulate an AI agent, for example because its source code is known. Our aim is to explore ways of leveraging this possibility to achieve more cooperative outcomes in strategic settings. In this paper, we study an interaction between AI agents where the agents run a recursive joint simulation. That is, the agents first jointly observe a simulation of the situation they face. This simulation in turn recursively includes additional simulations (with a small chance of failure, to avoid infinite recursion), and the results of all these nested simulations are observed before an action is chosen. We show that the resulting interaction is strategically equivalent to an infinitely repeated version of the original game, allowing a direct transfer of existing results such as the various folk theorems.

A Theory of Bounded Inductive Rationality

The dominant theories of rational choice assume logical omniscience. That is, they assume that when facing a decision problem, an agent can perform all relevant computations and determine the truth value of all relevant logical/mathematical claims. This assumption is unrealistic when, for example, we offer bets on remote digits of pi or when an agent faces a computationally intractable planning problem. Furthermore, the assumption of logical omniscience creates contradictions in cases where the environment can contain descriptions of the agent itself. Importantly, strategic interactions as studied in game theory are decision problems in which a rational agent is predicted by its environment (the other players). In this paper, we develop a theory of rational decision making that does not assume logical omniscience. We consider agents who repeatedly face decision problems (including ones like betting on digits of pi or games against other agents). The main contribution of this paper is to provide a sensible theory of rationality for such agents. Roughly, we require that a boundedly rational inductive agent tests each efficiently computable hypothesis infinitely often and follows those hypotheses that keep their promises of high rewards. We then prove that agents that are rational in this sense have other desirable properties. For example, they learn to value random and pseudo-random lotteries at their expected reward. Finally, we consider strategic interactions between different agents and prove a folk theorem for what strategies bounded rational inductive agents can converge to.

The Computational Complexity of Single-Player Imperfect-Recall Games

We study single-player extensive-form games with imperfect recall, such as the Sleeping Beauty problem or the Absentminded Driver game. For such games, two natural equilibrium concepts have been proposed as alternative solution concepts to ex-ante optimality. One equilibrium concept uses generalized double halving (GDH) as a belief system and evidential decision theory (EDT), and another one uses generalized thirding (GT) as a belief system and causal decision theory (CDT). Our findings relate those three solution concepts of a game to solution concepts of a polynomial maximization problem: global optima, optimal points with respect to subsets of variables and Karush-Kuhn-Tucker (KKT) points. Based on these correspondences, we are able to settle various complexity-theoretic questions on the computation of such strategies. For ex-ante optimality and (EDT,GDH)-equilibria, we obtain NP-hardness and inapproximability, and for (CDT,GT)-equilibria we obtain CLS-completeness results.