arXiv subjects

Alistair Letcher

Publications and source records attributed to Alistair Letcher.

15 recordsLinked to original sources

arXiv2026

DiscoGen: Procedural Generation of Algorithm Discovery Tasks in Machine Learning

Automating the development of machine learning algorithms has the potential to unlock new breakthroughs. However, our ability to improve and evaluate algorithm discovery systems has thus far been limited by existing task suites. They suffer from many issues, such as: poor evaluation methodologies; data contamination; and containing saturated or very similar problems. Here, we introduce DiscoGen, a procedural generator of algorithm discovery tasks for machine learning, such as developing optimisers for reinforcement learning or loss functions for image classification. Motivated by the success of procedural generation in reinforcement learning, DiscoGen spans billions of tasks of varying difficulty and complexity from a range of machine learning fields. These tasks are specified by a small number of configuration parameters and can be used to optimise algorithm discovery agents (ADAs). We present DiscoBench, a fixed, small subset of DiscoGen tasks for principled evaluation of ADAs. Finally, we propose a number of ambitious, impactful research directions enabled by DiscoGen, and demonstrate its use for ADA optimisation through scaling experiments for automated prompt tuning. DiscoGen is released open-source at https://github.com/AlexGoldie/discogen.

cs.LG↗

arXiv2026

Inverting the Bellman Equation: From $Q$-Values to World Models

Model-based and model-free reinforcement learning are traditionally viewed as separate paradigms: instead of learning a model of the transition kernel $P$, model-free agents typically estimate value functions tied to a specific policy and reward. In this paper, we challenge this dichotomy by proving that value-based agents trained on a sufficiently rich set of reward functions, e.g. using goal-conditioned RL, implicitly encode a unique and accurate world model. To extract this model in practice, we introduce \textit{$P$-learning}, an inverse analogue to $Q$-learning that samples from an agent's $Q$-values, policies and rewards to decode its internal model of the environment. We then provide sufficient conditions on the type and number of goals for which agents encode the true kernel $P$, covering both stochastic and deterministic MDPs over finite or continuous state spaces. Even when our assumptions are violated, we empirically demonstrate that agents trained on a handful of reward functions encode accurate dynamics in $\texttt{Reacher}$, $\texttt{MountainCar}$ and stochastic variants of $\texttt{FourRooms}$. Surprisingly, we find that policies trained exclusively on a \texttt{Reacher} agent's implicit world model are quasi-optimal on out-of-distribution, velocity-based goals despite position-only training -- suggesting that agents contain hidden generalisation capabilities and providing a new lens into the connection between model-based, model-free, and goal-conditioned RL.

cs.LG↗

arXiv2026

Goal-Conditioned Agents that Learn Everything All at Once

A goal-conditioned reinforcement learning agent exploring an environment will see a wealth of information throughout a trajectory, most of which is discarded when only performing on-policy updates with respect to the commanded goal. All-goals learning, where each transition is used for learning off-policy with respect to every goal, allows agents to extract maximal information, however it is usually computationally infeasible when done via naive relabelling. This can be overcome by jointly outputting values and actions for every goal at once, allowing for efficient, parallel all-goals updates with a single pass through the network, in a process we call Learning Everything all at Once (LEO). We show that this approach significantly outperforms other methods on goal-conditioned Craftax and is competitive with existing baselines on continuous control environments, while achieving a >250x speed-up compared to all-goals relabelling. We then go on to show that this approach can be made even more powerful by using LEO as a teacher network, rather than a direct actor. We hope that, by unlocking all-goals learning at scale, LEO can serve as a useful tool for RL practitioners in complex environments. We open source our code.

cs.LG↗

arXiv2026

Evolution Strategies at the Hyperscale

Evolution Strategies (ES) is a class of powerful black-box optimisation methods that are highly parallelisable and can handle non-differentiable and noisy objectives. However, naïve ES becomes prohibitively expensive at scale on GPUs due to the low arithmetic intensity of batched matrix multiplications with unstructured random perturbations. We introduce Evolution Guided GeneRal Optimisation via Low-rank Learning (EGGROLL), which improves arithmetic intensity by structuring individual perturbations as rank-$r$ matrices, resulting in a hundredfold increase in training speed for billion-parameter models at large population sizes, achieving up to 91% of the throughput of pure batch inference. We provide a rigorous theoretical analysis of Gaussian ES for high-dimensional parameter objectives, investigating conditions needed for ES updates to converge in high dimensions. Our results reveal a linearising effect, and proving consistency between EGGROLL and ES as parameter dimension increases. Our experiments show that EGGROLL: (1) enables the stable pretraining of nonlinear recurrent language models that operate purely in integer datatypes, (2) is competitive with GRPO for post-training LLMs on reasoning tasks, and (3) does not compromise performance compared to ES in tabula rasa RL settings, despite being faster.

cs.LG↗

arXiv2025

An Optimisation Framework for Unsupervised Environment Design

For reinforcement learning agents to be deployed in high-risk settings, they must achieve a high level of robustness to unfamiliar scenarios. One method for improving robustness is unsupervised environment design (UED), a suite of methods aiming to maximise an agent's generalisability across configurations of an environment. In this work, we study UED from an optimisation perspective, providing stronger theoretical guarantees for practical settings than prior work. Whereas previous methods relied on guarantees if they reach convergence, our framework employs a nonconvex-strongly-concave objective for which we provide a provably convergent algorithm in the zero-sum setting. We empirically verify the efficacy of our method, outperforming prior methods in a number of environments with varying difficulties.

cs.LG↗

arXiv2024

Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits

The training of a parameterized model largely depends on the landscape of the underlying loss function. In particular, vanishing gradients are a central bottleneck in the scalability of variational quantum algorithms (VQAs), and are known to arise in various ways. However, a caveat of most existing gradient bound results is the requirement of t-design circuit assumptions that are typically not satisfied in practice. In this work, we loosen these assumptions altogether and derive tight upper and lower bounds on loss and gradient concentration for a large class of parameterized quantum circuits and arbitrary observables, which are significantly stronger than prior work. Moreover, we show that these bounds, as well as the variance of the loss itself, can be estimated efficiently and classically-providing practical tools to study the loss landscapes of VQA models, including verifying whether or not a circuit/observable induces barren plateaus. In particular, our results can readily be leveraged to rule out barren plateaus for a realistic class of ansätze and mixed observables, namely, observables containing a non-vanishing local term. This insight has direct implications for hybrid Quantum Generative Adversarial Networks (qGANs). We prove that designing the discriminator appropriately leads to 1-local weights that stay constant in the number of qubits, regardless of discriminator depth. This implies that qGANs with appropriately chosen generators do not suffer from barren plateaus even at scale-making them a promising candidate for applications in generative quantum machine learning. We demonstrate this result by training a qGAN to learn a 2D mixture of Gaussian distributions with up to 16 qubits, and provide numerical evidence that global contributions to the gradient, while initially exponentially small, may kick in substantially over the course of training.

quant-ph↗

arXiv2023

Adversarial Cheap Talk

Adversarial attacks in reinforcement learning (RL) often assume highly-privileged access to the victim's parameters, environment, or data. Instead, this paper proposes a novel adversarial setting called a Cheap Talk MDP in which an Adversary can merely append deterministic messages to the Victim's observation, resulting in a minimal range of influence. The Adversary cannot occlude ground truth, influence underlying environment dynamics or reward signals, introduce non-stationarity, add stochasticity, see the Victim's actions, or access their parameters. Additionally, we present a simple meta-learning algorithm called Adversarial Cheap Talk (ACT) to train Adversaries in this setting. We demonstrate that an Adversary trained with ACT still significantly influences the Victim's training and testing performance, despite the highly constrained setting. Affecting train-time performance reveals a new attack vector and provides insight into the success and failure modes of existing RL algorithms. More specifically, we show that an ACT Adversary is capable of harming performance by interfering with the learner's function approximation, or instead helping the Victim's performance by outputting useful features. Finally, we show that an ACT Adversary can manipulate messages during train-time to directly and arbitrarily control the Victim at test-time. Project video and code are available at https://sites.google.com/view/adversarial-cheap-talk

cs.LG↗

arXiv2022

Discovered Policy Optimisation

Tremendous progress has been made in reinforcement learning (RL) over the past decade. Most of these advancements came through the continual development of new algorithms, which were designed using a combination of mathematical derivations, intuitions, and experimentation. Such an approach of creating algorithms manually is limited by human understanding and ingenuity. In contrast, meta-learning provides a toolkit for automatic machine learning method optimisation, potentially addressing this flaw. However, black-box approaches which attempt to discover RL algorithms with minimal prior structure have thus far not outperformed existing hand-crafted algorithms. Mirror Learning, which includes RL algorithms, such as PPO, offers a potential middle-ground starting point: while every method in this framework comes with theoretical guarantees, components that differentiate them are subject to design. In this paper we explore the Mirror Learning space by meta-learning a "drift" function. We refer to the immediate result as Learnt Policy Optimisation (LPO). By analysing LPO we gain original insights into policy optimisation which we use to formulate a novel, closed-form RL algorithm, Discovered Policy Optimisation (DPO). Our experiments in Brax environments confirm state-of-the-art performance of LPO and DPO, as well as their transfer to unseen settings.

cs.LG↗

arXiv2022

COLA: Consistent Learning with Opponent-Learning Awareness

Learning in general-sum games is unstable and frequently leads to socially undesirable (Pareto-dominated) outcomes. To mitigate this, Learning with Opponent-Learning Awareness (LOLA) introduced opponent shaping to this setting, by accounting for each agent's influence on their opponents' anticipated learning steps. However, the original LOLA formulation (and follow-up work) is inconsistent because LOLA models other agents as naive learners rather than LOLA agents. In previous work, this inconsistency was suggested as a cause of LOLA's failure to preserve stable fixed points (SFPs). First, we formalize consistency and show that higher-order LOLA (HOLA) solves LOLA's inconsistency problem if it converges. Second, we correct a claim made in the literature by Schäfer and Anandkumar (2019), proving that Competitive Gradient Descent (CGD) does not recover HOLA as a series expansion (and fails to solve the consistency problem). Third, we propose a new method called Consistent LOLA (COLA), which learns update functions that are consistent under mutual opponent shaping. It requires no more than second-order derivatives and learns consistent update functions even when HOLA fails to converge. However, we also prove that even consistent update functions do not preserve SFPs, contradicting the hypothesis that this shortcoming is caused by LOLA's inconsistency. Finally, in an empirical evaluation on a set of general-sum games, we find that COLA finds prosocial solutions and that it converges under a wider range of learning rates than HOLA and LOLA. We support the latter finding with a theoretical result for a simple game.

cs.LG↗

arXiv2021

Polymatrix Competitive Gradient Descent

Many economic games and machine learning approaches can be cast as competitive optimization problems where multiple agents are minimizing their respective objective function, which depends on all agents' actions. While gradient descent is a reliable basic workhorse for single-agent optimization, it often leads to oscillation in competitive optimization. In this work we propose polymatrix competitive gradient descent (PCGD) as a method for solving general sum competitive optimization involving arbitrary numbers of agents. The updates of our method are obtained as the Nash equilibria of a local polymatrix approximation with a quadratic regularization, and can be computed efficiently by solving a linear system of equations. We prove local convergence of PCGD to stable fixed points for $n$-player general-sum games, and show that it does not require adapting the step size to the strength of the player-interactions. We use PCGD to optimize policies in multi-agent reinforcement learning and demonstrate its advantages in Snake, Markov soccer and an electricity market game. Agents trained by PCGD outperform agents trained with simultaneous gradient descent, symplectic gradient adjustment, and extragradient in Snake and Markov soccer games and on the electricity market game, PCGD trains faster than both simultaneous gradient descent and the extragradient method.

cs.LG↗

arXiv2021

Stable Opponent Shaping in Differentiable Games

A growing number of learning methods are actually differentiable games whose players optimise multiple, interdependent objectives in parallel -- from GANs and intrinsic curiosity to multi-agent RL. Opponent shaping is a powerful approach to improve learning dynamics in these games, accounting for player influence on others' updates. Learning with Opponent-Learning Awareness (LOLA) is a recent algorithm that exploits this response and leads to cooperation in settings like the Iterated Prisoner's Dilemma. Although experimentally successful, we show that LOLA agents can exhibit 'arrogant' behaviour directly at odds with convergence. In fact, remarkably few algorithms have theoretical guarantees applying across all (n-player, non-convex) games. In this paper we present Stable Opponent Shaping (SOS), a new method that interpolates between LOLA and a stable variant named LookAhead. We prove that LookAhead converges locally to equilibria and avoids strict saddles in all differentiable games. SOS inherits these essential guarantees, while also shaping the learning of opponents and consistently either matching or outperforming LOLA experimentally.

cs.MA↗

arXiv2021

On the Impossibility of Global Convergence in Multi-Loss Optimization

Under mild regularity conditions, gradient-based methods converge globally to a critical point in the single-loss setting. This is known to break down for vanilla gradient descent when moving to multi-loss optimization, but can we hope to build some algorithm with global guarantees? We negatively resolve this open problem by proving that desirable convergence properties cannot simultaneously hold for any algorithm. Our result has more to do with the existence of games with no satisfactory outcomes, than with algorithms per se. More explicitly we construct a two-player game with zero-sum interactions whose losses are both coercive and analytic, but whose only simultaneous critical point is a strict maximum. Any 'reasonable' algorithm, defined to avoid strict maxima, will therefore fail to converge. This is fundamentally different from single losses, where coercivity implies existence of a global minimum. Moreover, we prove that a wide range of existing gradient-based methods almost surely have bounded but non-convergent iterates in a constructed zero-sum game for suitably small learning rates. It nonetheless remains an open question whether such behavior can arise in high-dimensional games of interest to ML practitioners, such as GANs or multi-agent RL.

math.OC↗

arXiv2020

Ridge Rider: Finding Diverse Solutions by Following Eigenvectors of the Hessian

Over the last decade, a single algorithm has changed many facets of our lives - Stochastic Gradient Descent (SGD). In the era of ever decreasing loss functions, SGD and its various offspring have become the go-to optimization tool in machine learning and are a key component of the success of deep neural networks (DNNs). While SGD is guaranteed to converge to a local optimum (under loose assumptions), in some cases it may matter which local optimum is found, and this is often context-dependent. Examples frequently arise in machine learning, from shape-versus-texture-features to ensemble methods and zero-shot coordination. In these settings, there are desired solutions which SGD on 'standard' loss functions will not find, since it instead converges to the 'easy' solutions. In this paper, we present a different approach. Rather than following the gradient, which corresponds to a locally greedy direction, we instead follow the eigenvectors of the Hessian, which we call "ridges". By iteratively following and branching amongst the ridges, we effectively span the loss surface to find qualitatively different solutions. We show both theoretically and experimentally that our method, called Ridge Rider (RR), offers a promising direction for a variety of challenging problems.

cs.LG↗

arXiv2019

Differentiable Game Mechanics

Deep learning is built on the foundational guarantee that gradient descent on an objective function converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, that exhibit multiple interacting losses. The behavior of gradient-based methods in games is not well understood -- and is becoming increasingly important as adversarial and multi-objective architectures proliferate. In this paper, we develop new tools to understand and control the dynamics in n-player differentiable games. The key result is to decompose the game Jacobian into two components. The first, symmetric component, is related to potential games, which reduce to gradient descent on an implicit function. The second, antisymmetric component, relates to Hamiltonian games, a new class of games that obey a conservation law akin to conservation laws in classical mechanical systems. The decomposition motivates Symplectic Gradient Adjustment (SGA), a new algorithm for finding stable fixed points in differentiable games. Basic experiments show SGA is competitive with recently proposed algorithms for finding stable fixed points in GANs -- while at the same time being applicable to, and having guarantees in, much more general cases.

cs.LG↗

arXiv2018

Automatic Conflict Detection in Police Body-Worn Audio

Automatic conflict detection has grown in relevance with the advent of body-worn technology, but existing metrics such as turn-taking and overlap are poor indicators of conflict in police-public interactions. Moreover, standard techniques to compute them fall short when applied to such diversified and noisy contexts. We develop a pipeline catered to this task combining adaptive noise removal, non-speech filtering and new measures of conflict based on the repetition and intensity of phrases in speech. We demonstrate the effectiveness of our approach on body-worn audio data collected by the Los Angeles Police Department.

eess.AS↗