Since human planning systematically deviates from rationality, several approaches have been tried to account for specific human shortcomings. However, the general problem of inferring the reward function of an agent of unknown rationality has received little attention. Unlike the well-known ambiguity problems in IRL, this one is practically relevant but cannot be resolved by observing the agent's policy in enough environments. This paper shows (1) that a No Free Lunch result implies it is impossible to uniquely decompose a policy into a planning algorithm and reward function, and (2) that even with a reasonable simplicity prior/Occam's razor on the set of decompositions, we cannot distinguish between the true decomposition and others that lead to high regret. To address this, we need simple `normative' assumptions, which cannot be deduced exclusively from observations.

What makes a classifier have the ability to generalize? There have been a lot of important attempts to address this question, but a clear answer is still elusive. Proponents of complexity theory find that the complexity of the classifier's function space is key to deciding generalization, whereas other recent work reveals that classifiers which extract invariant feature representations are likely to generalize better. Recent theoretical and empirical studies, however, have shown that even within a classifier's function space, there can be significant differences in the ability to generalize. Specifically, empirical studies have shown that among functions which have a good training data fit, functions with lower Kolmogorov complexity (KC) are likely to generalize better, while the opposite is true for functions of higher KC.

State-of-the-art deep neural networks are still struggling to address the catastrophic forgetting problem in continual learning. In this paper, we propose one simple paradigm (named as S-Prompting) and two concrete approaches to highly reduce the forgetting degree in one of the most typical continual learning scenarios, i.e., domain increment learning (DIL). The key idea of the paradigm is to learn prompts independently across domains with pre-trained transformers, avoiding the use of exemplars that commonly appear in conventional methods. This results in a win-win game where the prompting can achieve the best for each domain.

Large language models have recently shown a remarkable ability for few-shot learning, including patterns of algorithmic nature. However, it is still an open question to determine what kind of patterns these models can capture and how many examples they need in their prompts. We frame this question as a teaching problem with strong priors, and study whether language models can identify simple algorithmic concepts from small witness sets. In particular, we explore how several GPT architectures, program induction systems and humans perform in terms of the complexity of the concept and the number of additional examples, and how much their behaviour differs. This first joint analysis of language models and machine teaching can address key questions for artificial intelligence and machine learning, such as whether some strong priors, and Occam's razor in particular, can be distilled from data, making learning from a few examples possible.

The Best Razor I've Ever Used Is on Sale Henson Razors are engineered to give a spectacular shave with dirt-cheap generic blades. Razors are one of the most heavily and competitively marketed products in American capitalism. Made with steel and plastic that costs a few pennies, but sold for a thousand percent profit, the razor market is the subject of vigorous academic study and debate. The founder of Gillette famously came up with a model of basically giving away the razor handle so he could sell the blades. Canadian startup Henson has the opposite model, charging $79 for a razor that can give you an excellent shave with dirt-cheap disposable blades that cost about 15 cents each .

Since human planning systematically deviates from rationality, several approaches have been tried to account for specific human shortcomings. However, the general problem of inferring the reward function of an agent of unknown rationality has received little attention. Unlike the well-known ambiguity problems in IRL, this one is practically relevant but cannot be resolved by observing the agent's policy in enough environments. This paper shows (1) that a No Free Lunch result implies it is impossible to uniquely decompose a policy into a planning algorithm and reward function, and (2) that even with a reasonable simplicity prior/Occam's razor on the set of decompositions, we cannot distinguish between the true decomposition and others that lead to high regret. To address this, we need simple `normative' assumptions, which cannot be deduced exclusively from observations.

We include some other experiments not described in the paper.

The integration of the history and philosophy of statistics was initiated at least by Hacking (1975) and advanced by Hacking (1990), Mayo (1996), and Zabell (2005), but it has not received sustained follow-up. Yet such integration is more urgent than ever, as the recent success of artificial intelligence has been driven largely by machine learning -- a field historically developed alongside statistics. Today, the boundary between statistics and machine learning is increasingly blurred. What we now need is integration, twice over: of history and philosophy, and of two fields they engage -- statistics and machine learning. I present a case study of a philosophical idea in machine learning (and in formal epistemology) whose root can be traced back to an often under-appreciated insight in Neyman and Pearson's 1936 work (a follow-up to their 1933 classic). This leads to the articulation of an epistemological principle -- largely implicit in, but shared by, the practices of frequentist statistics and machine learning -- which I call achievabilism: the thesis that the correct standard for assessing non-deductive inference methods should not be fixed, but should instead be sensitive to what is achievable in specific problem contexts. Another integration also emerges at the level of methodology, combining two ends of the philosophy of science spectrum: history and philosophy of science on the one hand, and formal epistemology on the other hand.

Symmetries have proven useful in machine learning models, improving generalisation and overall performance. At the same time, recent advancements in learning dynamical systems rely on modelling the underlying Hamiltonian to guarantee the conservation of energy.These approaches can be connected via a seminal result in mathematical physics: Noether's theorem, which states that symmetries in a dynamical system correspond to conserved quantities.This work uses Noether's theorem to parameterise symmetries as learnable conserved quantities. We then allow conserved quantities and associated symmetries to be learned directly from train data through approximate Bayesian model selection, jointly with the regular training procedure. As training objective, we derive a variational lower bound to the marginal likelihood. The objective automatically embodies an Occam's Razor effect that avoids collapse of conversation laws to the trivial constant, without the need to manually add and tune additional regularisers.