arXiv subjects

Lars Buesing

Publications and source records attributed to Lars Buesing.

At least 19 recordsLinked to original sources

arXiv2026

AI co-mathematician: Accelerating mathematicians with agentic AI

We introduce the AI co-mathematician, a workbench for mathematicians to interactively leverage AI agents to pursue open-ended research. The AI co-mathematician is optimized to provide holistic support for the exploratory and iterative reality of mathematical workflows, including ideation, literature search, computational exploration, theorem proving and theory building. By providing an asynchronous, stateful workspace that manages uncertainty, refines user intent, tracks failed hypotheses, and outputs native mathematical artifacts, the system mirrors human collaborative workflows. In early tests, the AI co-mathematician helped researchers solve open problems, identify new research directions, and uncover overlooked literature references. Besides demonstrating a highly interactive paradigm for AI-assisted mathematical discovery, the AI co-mathematician also achieves state of the art results on hard problem-solving benchmarks, including scoring 48% on FrontierMath Tier 4, a new high score among all AI systems evaluated.

cs.AI↗

arXiv2024

Amplifying human performance in combinatorial competitive programming

Recent years have seen a significant surge in complex AI systems for competitive programming, capable of performing at admirable levels against human competitors. While steady progress has been made, the highest percentiles still remain out of reach for these methods on standard competition platforms such as Codeforces. Here we instead focus on combinatorial competitive programming, where the target is to find as-good-as-possible solutions to otherwise computationally intractable problems, over specific given inputs. We hypothesise that this scenario offers a unique testbed for human-AI synergy, as human programmers can write a backbone of a heuristic solution, after which AI can be used to optimise the scoring function used by the heuristic. We deploy our approach on previous iterations of Hash Code, a global team programming competition inspired by NP-hard software engineering problems at Google, and we leverage FunSearch to evolve our scoring functions. Our evolved solutions significantly improve the attained scores from their baseline, successfully breaking into the top percentile on all previous Hash Code online qualification rounds, and outperforming the top human teams on several. Our method is also performant on an optimisation problem that featured in a recent held-out AtCoder contest.

cs.LG↗

arXiv2022

Pushing the limits of self-supervised ResNets: Can we outperform supervised learning without labels on ImageNet?

Despite recent progress made by self-supervised methods in representation learning with residual networks, they still underperform supervised learning on the ImageNet classification benchmark, limiting their applicability in performance-critical settings. Building on prior theoretical insights from ReLIC [Mitrovic et al., 2021], we include additional inductive biases into self-supervised learning. We propose a new self-supervised representation learning method, ReLICv2, which combines an explicit invariance loss with a contrastive objective over a varied set of appropriately constructed data views to avoid learning spurious correlations and obtain more informative representations. ReLICv2 achieves $77.1\%$ top-$1$ accuracy on ImageNet under linear evaluation on a ResNet50, thus improving the previous state-of-the-art by absolute $+1.5\%$; on larger ResNet models, ReLICv2 achieves up to $80.6\%$ outperforming previous self-supervised approaches with margins up to $+2.3\%$. Most notably, ReLICv2 is the first unsupervised representation learning method to consistently outperform the supervised baseline in a like-for-like comparison over a range of ResNet architectures. Using ReLICv2, we also learn more robust and transferable representations that generalize better out-of-distribution than previous work, both on image classification and semantic segmentation. Finally, we show that despite using ResNet encoders, ReLICv2 is comparable to state-of-the-art self-supervised vision transformers.

cs.CV↗

arXiv2021

Towards combinatorial invariance for Kazhdan-Lusztig polynomials

Kazhdan-Lusztig polynomials are important and mysterious objects in representation theory. Here we present a new formula for their computation for symmetric groups based on the Bruhat graph. Our approach suggests a solution to the combinatorial invariance conjecture for symmetric groups, a well-known conjecture formulated by Lusztig and Dyer in the 1980s.

math.RT↗

arXiv2020

Counterfactual Credit Assignment in Model-Free Reinforcement Learning

Credit assignment in reinforcement learning is the problem of measuring an action's influence on future rewards. In particular, this requires separating skill from luck, i.e. disentangling the effect of an action on rewards from that of external factors and subsequent actions. To achieve this, we adapt the notion of counterfactuals from causality theory to a model-free RL setup. The key idea is to condition value functions on future events, by learning to extract relevant information from a trajectory. We formulate a family of policy gradient algorithms that use these future-conditional value functions as baselines or critics, and show that they are provably low variance. To avoid the potential bias from conditioning on future information, we constrain the hindsight information to not contain information about the agent's actions. We demonstrate the efficacy and validity of our algorithm on a number of illustrative and challenging problems.

cs.LG↗

arXiv2020

On the role of planning in model-based deep reinforcement learning

Model-based planning is often thought to be necessary for deep, careful reasoning and generalization in artificial agents. While recent successes of model-based reinforcement learning (MBRL) with deep function approximation have strengthened this hypothesis, the resulting diversity of model-based methods has also made it difficult to track which components drive success and why. In this paper, we seek to disentangle the contributions of recent methods by focusing on three questions: (1) How does planning benefit MBRL agents? (2) Within planning, what choices drive performance? (3) To what extent does planning improve generalization? To answer these questions, we study the performance of MuZero (Schrittwieser et al., 2019), a state-of-the-art MBRL algorithm with strong connections and overlapping components with many other MBRL algorithms. We perform a number of interventions and ablations of MuZero across a wide range of environments, including control tasks, Atari, and 9x9 Go. Our results suggest the following: (1) Planning is most useful in the learning process, both for policy updates and for providing a more useful data distribution. (2) Using shallow trees with simple Monte-Carlo rollouts is as performant as more complex methods, except in the most difficult reasoning tasks. (3) Planning alone is insufficient to drive strong generalization. These results indicate where and how to utilize planning in reinforcement learning settings, and highlight a number of open questions for future MBRL research.

cs.AI↗

arXiv2020

Representation Learning via Invariant Causal Mechanisms

Self-supervised learning has emerged as a strategy to reduce the reliance on costly supervised signal by pretraining representations only using unlabeled data. These methods combine heuristic proxy classification tasks with data augmentations and have achieved significant success, but our theoretical understanding of this success remains limited. In this paper we analyze self-supervised representation learning using a causal framework. We show how data augmentations can be more effectively utilized through explicit invariance constraints on the proxy classifiers employed during pretraining. Based on this, we propose a novel self-supervised objective, Representation Learning via Invariant Causal Mechanisms (ReLIC), that enforces invariant prediction of proxy targets across augmentations through an invariance regularizer which yields improved generalization guarantees. Further, using causality we generalize contrastive learning, a particular kind of self-supervised method, and provide an alternative theoretical explanation for the success of these methods. Empirically, ReLIC significantly outperforms competing methods in terms of robustness and out-of-distribution generalization on ImageNet, while also significantly outperforming these methods on Atari achieving above human-level performance on $51$ out of $57$ games.

cs.LG↗

arXiv2020

Beyond Tabula-Rasa: a Modular Reinforcement Learning Approach for Physically Embedded 3D Sokoban

Intelligent robots need to achieve abstract objectives using concrete, spatiotemporally complex sensory information and motor control. Tabula rasa deep reinforcement learning (RL) has tackled demanding tasks in terms of either visual, abstract, or physical reasoning, but solving these jointly remains a formidable challenge. One recent, unsolved benchmark task that integrates these challenges is Mujoban, where a robot needs to arrange 3D warehouses generated from 2D Sokoban puzzles. We explore whether integrated tasks like Mujoban can be solved by composing RL modules together in a sense-plan-act hierarchy, where modules have well-defined roles similarly to classic robot architectures. Unlike classic architectures that are typically model-based, we use only model-free modules trained with RL or supervised learning. We find that our modular RL approach dramatically outperforms the state-of-the-art monolithic RL agent on Mujoban. Further, learned modules can be reused when, e.g., using a different robot platform to solve the same task. Together our results give strong evidence for the importance of research into modular RL designs. Project website: https://sites.google.com/view/modular-rl/

cs.LG↗

arXiv2020

Physically Embedded Planning Problems: New Challenges for Reinforcement Learning

Recent work in deep reinforcement learning (RL) has produced algorithms capable of mastering challenging games such as Go, chess, or shogi. In these works the RL agent directly observes the natural state of the game and controls that state directly with its actions. However, when humans play such games, they do not just reason about the moves but also interact with their physical environment. They understand the state of the game by looking at the physical board in front of them and modify it by manipulating pieces using touch and fine-grained motor control. Mastering complicated physical systems with abstract goals is a central challenge for artificial intelligence, but it remains out of reach for existing RL algorithms. To encourage progress towards this goal we introduce a set of physically embedded planning problems and make them publicly available. We embed challenging symbolic tasks (Sokoban, tic-tac-toe, and Go) in a physics engine to produce a set of tasks that require perception, reasoning, and motor control over long time horizons. Although existing RL algorithms can tackle the symbolic versions of these tasks, we find that they struggle to master even the simplest of their physically embedded counterparts. As a first step towards characterizing the space of solution to these tasks, we introduce a strong baseline that uses a pre-trained expert game player to provide hints in the abstract space to an RL agent's policy while training it on the full sensorimotor control task. The resulting agent solves many of the tasks, underlining the need for methods that bridge the gap between abstract planning and embodied control. See illustrating video at https://youtu.be/RwHiHlym_1k.

cs.AI↗

arXiv2020

Pointer Graph Networks

Graph neural networks (GNNs) are typically applied to static graphs that are assumed to be known upfront. This static input structure is often informed purely by insight of the machine learning practitioner, and might not be optimal for the actual task the GNN is solving. In absence of reliable domain expertise, one might resort to inferring the latent graph structure, which is often difficult due to the vast search space of possible graphs. Here we introduce Pointer Graph Networks (PGNs) which augment sets or graphs with additional inferred edges for improved model generalisation ability. PGNs allow each node to dynamically point to another node, followed by message passing over these pointers. The sparsity of this adaptable graph structure makes learning tractable while still being sufficiently expressive to simulate complex algorithms. Critically, the pointing mechanism is directly supervised to model long-term sequences of operations on classical data structures, incorporating useful structural inductive biases from theoretical computer science. Qualitatively, we demonstrate that PGNs can learn parallelisable variants of pointer-based data structures, namely disjoint set unions and link/cut trees. PGNs generalise out-of-distribution to 5x larger test inputs on dynamic graph connectivity tasks, outperforming unrestricted GNNs and Deep Sets.

stat.ML↗

arXiv2020

Divide-and-Conquer Monte Carlo Tree Search For Goal-Directed Planning

Standard planners for sequential decision making (including Monte Carlo planning, tree search, dynamic programming, etc.) are constrained by an implicit sequential planning assumption: The order in which a plan is constructed is the same in which it is executed. We consider alternatives to this assumption for the class of goal-directed Reinforcement Learning (RL) problems. Instead of an environment transition model, we assume an imperfect, goal-directed policy. This low-level policy can be improved by a plan, consisting of an appropriate sequence of sub-goals that guide it from the start to the goal state. We propose a planning algorithm, Divide-and-Conquer Monte Carlo Tree Search (DC-MCTS), for approximating the optimal plan by means of proposing intermediate sub-goals which hierarchically partition the initial tasks into simpler ones that are then solved independently and recursively. The algorithm critically makes use of a learned sub-goal proposal for finding appropriate partitions trees of new tasks based on prior experience. Different strategies for learning sub-goal proposals give rise to different planning strategies that strictly generalize sequential planning. We show that this algorithmic flexibility over planning order leads to improved results in navigation tasks in grid-worlds as well as in challenging continuous control environments.

cs.LG↗

arXiv2020

Value-driven Hindsight Modelling

Value estimation is a critical component of the reinforcement learning (RL) paradigm. The question of how to effectively learn value predictors from data is one of the major problems studied by the RL community, and different approaches exploit structure in the problem domain in different ways. Model learning can make use of the rich transition structure present in sequences of observations, but this approach is usually not sensitive to the reward function. In contrast, model-free methods directly leverage the quantity of interest from the future, but receive a potentially weak scalar signal (an estimate of the return). We develop an approach for representation learning in RL that sits in between these two extremes: we propose to learn what to model in a way that can directly help value prediction. To this end, we determine which features of the future trajectory provide useful information to predict the associated return. This provides tractable prediction targets that are directly relevant for a task, and can thus accelerate learning the value function. The idea can be understood as reasoning, in hindsight, about which aspects of the future observations could help past value prediction. We show how this can help dramatically even in simple policy evaluation settings. We then test our approach at scale in challenging domains, including on 57 Atari 2600 games.

cs.LG↗

arXiv2020

Causally Correct Partial Models for Reinforcement Learning

In reinforcement learning, we can learn a model of future observations and rewards, and use it to plan the agent's next actions. However, jointly modeling future observations can be computationally expensive or even intractable if the observations are high-dimensional (e.g. images). For this reason, previous works have considered partial models, which model only part of the observation. In this paper, we show that partial models can be causally incorrect: they are confounded by the observations they don't model, and can therefore lead to incorrect planning. To address this, we introduce a general family of partial models that are provably causally correct, yet remain fast because they do not need to fully model future observations.

cs.LG↗

arXiv2019

Combining Q-Learning and Search with Amortized Value Estimates

We introduce "Search with Amortized Value Estimates" (SAVE), an approach for combining model-free Q-learning with model-based Monte-Carlo Tree Search (MCTS). In SAVE, a learned prior over state-action values is used to guide MCTS, which estimates an improved set of state-action values. The new Q-estimates are then used in combination with real experience to update the prior. This effectively amortizes the value computation performed by MCTS, resulting in a cooperative relationship between model-free learning and model-based search. SAVE can be implemented on top of any Q-learning agent with access to a model, which we demonstrate by incorporating it into agents that perform challenging physical reasoning tasks and Atari. SAVE consistently achieves higher rewards with fewer training steps, and---in contrast to typical model-based search approaches---yields strong performance with very small search budgets. By combining real experience with information computed during search, SAVE demonstrates that it is possible to improve on both the performance of model-free learning and the computational cost of planning.

cs.LG↗

arXiv2019

Approximate Inference in Discrete Distributions with Monte Carlo Tree Search and Value Functions

A plethora of problems in AI, engineering and the sciences are naturally formalized as inference in discrete probabilistic models. Exact inference is often prohibitively expensive, as it may require evaluating the (unnormalized) target density on its entire domain. Here we consider the setting where only a limited budget of calls to the unnormalized density oracle is available, raising the challenge of where in the domain to allocate these function calls in order to construct a good approximate solution. We formulate this problem as an instance of sequential decision-making under uncertainty and leverage methods from reinforcement learning for probabilistic inference with budget constraints. In particular, we propose the TreeSample algorithm, an adaptation of Monte Carlo Tree Search to approximate inference. This algorithm caches all previous queries to the density oracle in an explicit search tree, and dynamically allocates new queries based on a "best-first" heuristic for exploration, using existing upper confidence bound methods. Our non-parametric inference method can be effectively combined with neural networks that compile approximate conditionals of the target, which are then used to guide the inference search and enable generalization across multiple target distributions. We show empirically that TreeSample outperforms standard approximate inference methods on synthetic factor graphs.

cs.LG↗

arXiv2019

Credit Assignment Techniques in Stochastic Computation Graphs

Stochastic computation graphs (SCGs) provide a formalism to represent structured optimization problems arising in artificial intelligence, including supervised, unsupervised, and reinforcement learning. Previous work has shown that an unbiased estimator of the gradient of the expected loss of SCGs can be derived from a single principle. However, this estimator often has high variance and requires a full model evaluation per data point, making this algorithm costly in large graphs. In this work, we address these problems by generalizing concepts from the reinforcement learning literature. We introduce the concepts of value functions, baselines and critics for arbitrary SCGs, and show how to use them to derive lower-variance gradient estimates from partial model evaluations, paving the way towards general and efficient credit assignment for gradient-based optimization. In doing so, we demonstrate how our results unify recent advances in the probabilistic inference and reinforcement learning literature.

cs.LG↗

arXiv2019

Temporal Difference Variational Auto-Encoder

To act and plan in complex environments, we posit that agents should have a mental simulator of the world with three characteristics: (a) it should build an abstract state representing the condition of the world; (b) it should form a belief which represents uncertainty on the world; (c) it should go beyond simple step-by-step simulation, and exhibit temporal abstraction. Motivated by the absence of a model satisfying all these requirements, we propose TD-VAE, a generative sequence model that learns representations containing explicit beliefs about states several steps into the future, and that can be rolled out directly without single-step transitions. TD-VAE is trained on pairs of temporally separated time points, using an analogue of temporal difference learning used in reinforcement learning.

cs.LG↗

arXiv2018

Woulda, Coulda, Shoulda: Counterfactually-Guided Policy Search

Learning policies on data synthesized by models can in principle quench the thirst of reinforcement learning algorithms for large amounts of real experience, which is often costly to acquire. However, simulating plausible experience de novo is a hard problem for many complex environments, often resulting in biases for model-based policy evaluation and search. Instead of de novo synthesis of data, here we assume logged, real experience and model alternative outcomes of this experience under counterfactual actions, actions that were not actually taken. Based on this, we propose the Counterfactually-Guided Policy Search (CF-GPS) algorithm for learning policies in POMDPs from off-policy experience. It leverages structural causal models for counterfactual evaluation of arbitrary policies on individual off-policy episodes. CF-GPS can improve on vanilla model-based RL algorithms by making use of available logged data to de-bias model predictions. In contrast to off-policy algorithms based on Importance Sampling which re-weight data, CF-GPS leverages a model to explicitly consider alternative outcomes, allowing the algorithm to make better use of experience data. We find empirically that these advantages translate into improved policy evaluation and search results on a non-trivial grid-world task. Finally, we show that CF-GPS generalizes the previously proposed Guided Policy Search and that reparameterization-based algorithms such Stochastic Value Gradient can be interpreted as counterfactual methods.

cs.LG↗