Prompting is one of the main ways to adapt a pretrained model to target tasks. Besides manually constructing prompts, many prompt optimization methods have been proposed in the literature. Method development is mainly empirically driven, with less emphasis on a conceptual understanding of prompting. In this paper we discuss how optimal prompting can be understood through a Bayesian view, which also implies some fundamental limitations of prompting that can only be overcome by tuning weights. The paper explains in detail how meta-trained neural networks behave as Bayesian predictors over the pretraining distribution, whose hallmark feature is rapid in-context adaptation. Optimal prompting can be studied formally as conditioning these Bayesian predictors, yielding criteria for target tasks where optimal prompting is and is not possible. We support the theory with educational experiments on LSTMs and Transformers, where we compare different versions of prefix-tuning and different weight-tuning methods. We also confirm that soft prefixes, which are sequences of real-valued vectors outside the token alphabet, can lead to very effective prompts for trained and even untrained networks by manipulating activations in ways that are not achievable by hard tokens. This adds an important mechanistic aspect beyond the conceptual Bayesian theory.

It has long been established that predictive models can be transformed into lossless compressors and vice versa. Incidentally, in recent years, the machine learning community has focused on training increasingly large and powerful self-supervised (language) models. Since these large language models exhibit impressive predictive capabilities, they are well-positioned to be strong compressors. In this work, we advocate for viewing the prediction problem through the lens of compression and evaluate the compression capabilities of large (foundation) models. We show that large language models are powerful general-purpose predictors and that the compression viewpoint provides novel insights into scaling laws, tokenization, and in-context learning. For example, Chinchilla 70B, while trained primarily on text, compresses ImageNet patches to 43.4% and LibriSpeech samples to 16.4% of their raw size, beating domain-specific compressors like PNG (58.5%) or FLAC (30.3%), respectively. Finally, we show that the prediction-compression equivalence allows us to use any compressor (like gzip) to build a conditional generative model.

Meta-learning has emerged as a powerful approach to train neural networks to learn new tasks quickly from limited data by pre-training them on a broad set of tasks. But, what are the limits of meta-learning? In this work, we explore the potential of amortizing the most powerful universal predictor, namely Solomonoff Induction (SI), into neural networks via leveraging (memory-based) meta-learning to its limits. We use Universal Turing Machines (UTMs) to generate training data used to expose networks to a broad range of patterns. We provide theoretical analysis of the UTM data generation processes and meta-training protocols. We conduct comprehensive experiments with neural architectures (e.g. LSTMs, Transformers) and algorithmic data generators of varying complexity and universality. Our results suggest that UTM data is a valuable resource for meta-learning, and that it can be used to train neural networks capable of learning universal prediction strategies.

Memory-based meta-learning is a technique for approximating Bayes-optimal predictors. Under fairly general conditions, minimizing sequential prediction error, measured by the log loss, leads to implicit meta-learning. The goal of this work is to investigate how far this interpretation can be realized by current sequence prediction models and training regimes. The focus is on piecewise stationary sources with unobserved switching-points, which arguably capture an important characteristic of natural language and action-observation sequences in partially observable environments. We show that various types of memory-based neural models, including Transformers, LSTMs, and RNNs can learn to accurately approximate known Bayes-optimal algorithms and behave as if performing Bayesian inference over the latent switching-points and the latent parameters governing the data distribution within each segment.

Levin Tree Search (LTS) is a search algorithm that makes use of a policy (a probability distribution over actions) and comes with a theoretical guarantee on the number of expansions before reaching a goal node, depending on the quality of the policy. This guarantee can be used as a loss function, which we call the LTS loss, to optimize neural networks representing the policy (LTS+NN). In this work we show that the neural network can be substituted with parameterized context models originating from the online compression literature (LTS+CM). We show that the LTS loss is convex under this new model, which allows for using standard convex optimization tools, and obtain convergence guarantees to the optimal parameters in an online setting for a given set of solution trajectories --- guarantees that cannot be provided for neural networks. The new LTS+CM algorithm compares favorably against LTS+NN on several benchmarks: Sokoban (Boxoban), The Witness, and the 24-Sliding Tile puzzle (STP). The difference is particularly large on STP, where LTS+NN fails to solve most of the test instances while LTS+CM solves each test instance in a fraction of a second. Furthermore, we show that LTS+CM is able to learn a policy that solves the Rubik's cube in only a few hundred expansions, which considerably improves upon previous machine learning techniques.

Traditional automated theorem proving systems for first-order logic depend on speed-optimized search and many handcrafted heuristics designed to work over a wide range of domains. Machine learning approaches in the literature either depend on these traditional provers to bootstrap themselves, by leveraging these heuristics, or can struggle due to limited existing proof data. The latter issue can be explained by the lack of a smooth difficulty gradient in theorem proving datasets; large gaps in difficulty between different theorems can make training harder or even impossible. In this paper, we adapt the idea of hindsight experience replay from reinforcement learning to the automated theorem proving domain, so as to use the intermediate data generated during unsuccessful proof attempts. We build a first-order logic prover by disabling all the smart clause-scoring heuristics of the state-of-the-art E prover and replacing them with a clause-scoring neural network learned by using hindsight experience replay in an incremental learning setting. Clauses are represented as graphs and presented to transformer networks with spectral features. We show that provers trained in this way can outperform previous machine learning approaches and compete with the state of the art heuristic-based theorem prover E in its best configuration, on the popular benchmarks MPTP2078, M2k and Mizar40. The proofs generated by our algorithm are also almost always significantly shorter than E’s proofs.

The use of a policy and a heuristic function for guiding search can be quite effective in adversarial problems, as demonstrated by AlphaGo and its successors, which are based on the PUCT search algorithm. While PUCT can also be used to solve single-agent deterministic problems, it lacks guarantees on its search effort and it can be computationally inefficient in practice. Combining the A* algorithm with a learned heuristic function tends to work better in these domains, but A* and its variants do not use a policy. Moreover, the purpose of using A* is to find solutions of minimum cost, while we seek instead to minimize the search loss (e.g., the number of search steps). LevinTS is guided by a policy and provides guarantees on the number of search steps that relate to the quality of the policy, but it does not make use of a heuristic function. In this work we introduce Policy-guided Heuristic Search (PHS), a novel search algorithm that uses both a heuristic function and a policy and has theoretical guarantees on the search loss that relates to both the quality of the heuristic and of the policy. We show empirically on the sliding-tile puzzle, Sokoban, and a puzzle from the commercial game `The Witness' that PHS enables the rapid learning of both a policy and a heuristic function and compares favorably with A*, Weighted A*, Greedy Best-First Search, LevinTS, and PUCT in terms of number of problems solved and search time in all three domains tested.

In some agent designs like inverse reinforcement learning an agent needs to learn its own reward function. Learning the reward function and optimising for it are typically two different processes, usually performed at different stages. We consider a continual (``one life'') learning approach where the agent both learns the reward function and optimises for it at the same time. We show that this comes with a number of pitfalls, such as deliberately manipulating the learning process in one direction, refusing to learn, ``learning'' facts already known to the agent, and making decisions that are strictly dominated (for all relevant reward functions). We formally introduce two desirable properties: the first is `unriggability', which prevents the agent from steering the learning process in the direction of a reward function that is easier to optimise. The second is `uninfluenceability', whereby the reward-function learning process operates by learning facts about the environment. We show that an uninfluenceable process is automatically unriggable, and if the set of possible environments is sufficiently large, the converse is true too.

Designing reward functions is difficult: the designer has to specify what to do (what it means to complete the task) as well as what not to do (side effects that should be avoided while completing the task). To alleviate the burden on the reward designer, we propose an algorithm to automatically generate an auxiliary reward function that penalizes side effects. This auxiliary objective rewards the ability to complete possible future tasks, which decreases if the agent causes side effects during the current task. The future task reward can also give the agent an incentive to interfere with events in the environment that make future tasks less achievable, such as irreversible actions by other agents. To avoid this interference incentive, we introduce a baseline policy that represents a default course of action (such as doing nothing), and use it to filter out future tasks that are not achievable by default. We formally define interference incentives and show that the future task approach with a baseline policy avoids these incentives in the deterministic case. Using gridworld environments that test for side effects and interference, we show that our method avoids interference and is more effective for avoiding side effects than the common approach of penalizing irreversible actions.

The Lottery Ticket Hypothesis is a conjecture that every large neural network contains a subnetwork that, when trained in isolation, achieves comparable performance to the large network. An even stronger conjecture has been proven recently: Every sufficiently overparameterized network contains a subnetwork that, even without training, achieves comparable accuracy to the trained large network. This theorem, however, relies on a number of strong assumptions and guarantees a polynomial factor on the size of the large network compared to the target function. In this work, we remove the most limiting assumptions of this previous work while providing significantly tighter bounds: the overparameterized network only needs a logarithmic factor (in all variables but depth) number of neurons per weight of the target subnetwork.

The field of reinforcement learning (RL) is facing increasingly challenging domains with combinatorial complexity. For an RL agent to address these challenges, it is essential that it can plan effectively. Prior work has typically utilized an explicit model of the environment, combined with a specific planning algorithm (such as tree search). More recently, a new family of methods have been proposed that learn how to plan, by providing the structure for planning via an inductive bias in the function approximator (such as a tree structured neural network), trained end-to-end by a model-free RL algorithm. In this paper, we go even further, and demonstrate empirically that an entirely model-free approach, without special structure beyond standard neural network components such as convolutional networks and LSTMs, can learn to exhibit many of the characteristics typically associated with a model-based planner. We measure our agent’s effectiveness at planning in terms of its ability to generalize across a combinatorial and irreversible state space, its data efficiency, and its ability to utilize additional thinking time. We find that our agent has many of the characteristics that one might expect to find in a planning algorithm. Furthermore, it exceeds the state-of-the-art in challenging combinatorial domains such as Sokoban and outperforms other model-free approaches that utilize strong inductive biases toward planning.

We tackle two long-standing problems related to re-expansions in heuristic search algorithms. For graph search, A* can require Ω(2ⁿ) expansions, where n is the number of states within the final f bound. Existing algorithms that address this problem like B and B’ improve this bound to Ω(n²). For tree search, IDA* can also require Ω(n²) expansions. We describe a new algorithmic framework that iteratively controls an expansion budget and solution cost limit, giving rise to new graph and tree search algorithms for which the number of expansions is O(n log C*), where C* is the optimal solution cost. Our experiments show that the new algorithms are robust in scenarios where existing algorithms fail. In the case of tree search, our new algorithms have no overhead over IDA* in scenarios to which IDA* is well suited and can therefore be recommended as a general replacement for IDA*.

We introduce two novel tree search algorithms that use a policy to guide search. The first algorithm is a best-first enumeration that uses a cost function that allows us to provide an upper bound on the number of nodes to be expanded before reaching a goal state. We show that this best-first algorithm is particularly well suited for ``needle-in-a-haystack'' problems. The second algorithm, which is based on sampling, provides an upper bound on the expected number of nodes to be expanded before reaching a set of goal states. We show that this algorithm is better suited for problems where many paths lead to a goal. We validate these tree search algorithms on 1,000 computer-generated levels of Sokoban, where the policy used to guide search comes from a neural network trained using A3C. Our results show that the policy tree search algorithms we introduce are competitive with a state-of-the-art domain-independent planner that uses heuristic search.

We consider prediction with expert advice under the log-loss with the goal of deriving efficient and robust algorithms. We argue that existing algorithms such as exponentiated gradient, online gradient descent and online Newton step do not adequately satisfy both requirements. Our main contribution is an analysis of the Prod algorithm that is robust to any data sequence and runs in linear time relative to the number of experts in each round. Despite the unbounded nature of the log-loss, we derive a bound that is independent of the largest loss and of the largest gradient, and depends only on the number of experts and the time horizon. Furthermore we give a Bayesian interpretation of Prod and adapt the algorithm to derive a tracking regret.

No real-world reward function is perfect. Sensory errors and software bugs may result in agents getting higher (or lower) rewards than they should. For example, a reinforcement learning agent may prefer states where a sensory error gives it the maximum reward, but where the true reward is actually small. We formalise this problem as a generalised Markov Decision Problem called Corrupt Reward MDP. Traditional RL methods fare poorly in CRMDPs, even under strong simplifying assumptions and when trying to compensate for the possibly corrupt rewards. Two ways around the problem are investigated. First, by giving the agent richer data, such as in inverse reinforcement learning and semi-supervised reinforcement learning, reward corruption stemming from systematic sensory errors may sometimes be completely managed. Second, by using randomisation to blunt the agent's optimisation, reward corruption can be partially managed under some assumptions.

We discuss some recent results on Thompson sampling for nonparametric reinforcement learning in countable classes of general stochastic environments. These environments can be non-Markovian, non-ergodic, and partially observable. We show that Thompson sampling learns the environment class in the sense that (1) asymptotically its value converges in mean to the optimal value and (2) given a recoverability assumption regret is sublinear. We conclude with a discussion about optimality in reinforcement learning.