arXiv subjects

Brendan O'Donoghue

Publications and source records attributed to Brendan O'Donoghue.

At least 19 recordsLinked to original sources

arXiv2026

How Transparent is DiffusionGemma?

LLM reasoning transparency is a critical affordance for understanding model decisions, mitigating misuse and misalignment, and debugging surprising model behaviors. However, DiffusionGemma performs a larger fraction of its computation in a continuous latent space; does this make its reasoning less transparent? We study this question by decomposing transparency into two components: variable transparency, whether we understand intermediate snapshots of a model's computational state; and algorithmic transparency, whether we can use these snapshots to reconstruct the process by which the model arrived at its outputs. Naively, DiffusionGemma has poor variable transparency: its opaque serial depth, the amount of serial computation that occurs in between interpretable model states, seems at first 28.6X higher than the corresponding autoregressive Gemma 4 model. However, we show that we can map the information flowing between denoising steps through an interpretable token bottleneck with no decrease in downstream performance. Treating these intermediate states as interpretable reduces the opaque serial depth to just 1.1X that of Gemma 4. Algorithmic transparency is harder for diffusion models than for autoregressive models because all token predictions in the canvas can change at every denoising step, giving the model the power to implement complicated distributed algorithms during the denoising process. To begin bridging this gap, we conduct a suite of interpretability case studies, uncovering initial evidence of novel diffusion-specific phenomena such as non-chronological reasoning, token and sequence smearing, and intermediate-context reasoning. Finally, we test monitorability, a key application of transparency that measures whether model outputs are useful for downstream tasks. We find that DiffusionGemma is similarly monitorable to Gemma 4.

cs.LG↗

arXiv2026

DiffusionGemma Technical Report

We introduce DiffusionGemma, an experimental open-weight language model that uses discrete diffusion to generate text at exceptionally high speed. Rather than decoding one token at a time, DiffusionGemma iteratively refines blocks of 256 tokens in parallel, avoiding the sequential decoding bottleneck of conventional autoregressive (AR) large language models. Instead of training from scratch, we obtain DiffusionGemma by fine-tuning the mixture-of-experts Gemma 4 model with 3.8B activated and 25.2B total parameters. Our compute-efficient two-stage training pipeline uses fewer than 10% of the starting AR model's total training token budget. The first stage uses supervised fine-tuning to teach bidirectional denoising, while the second stage combines reinforcement learning with sampler distillation to jointly improve generation quality and inference efficiency. DiffusionGemma establishes a new Pareto frontier for the trade-off between generation speed and model capability. Averaged across our full evaluation suite, it generates around 20 tokens per forward pass and achieves roughly 1,500 output tokens per second on a single NVIDIA H100 GPU, which is substantially faster than AR models even with state-of-the-art speculative decoding. DiffusionGemma also retains the starting model's support for thinking mode, multimodal inputs, and long contexts. Despite diffusion fine-tuning, it remains capable of AR generation with only minor performance degradation, suggesting a path toward hybrid diffusion-AR decoding.

cs.CL↗

arXiv2026

PDLP: A Practical First-Order Method for Large-Scale Linear Programming

We present PDLP, a practical first-order method for linear programming (LP) designed to solve large-scale LP problems. PDLP is based on the primal-dual hybrid gradient (PDHG) method applied to the minimax formulation of LP. PDLP incorporates several enhancements to PDHG, including diagonal preconditioning, presolving, adaptive step sizes, adaptive restarting, and feasibility polishing. Our algorithm is implemented in C++, available in Google's open-source OR-Tools library, and supports multithreading. To evaluate our method, we introduce a new collection of eleven large-scale LP problems with sizes ranging from 125 million to 6.3 billion nonzeros. PDLP solves eight of these instances to optimality gaps of 1% (with primal and dual feasibility errors of less than $10^{-8}$) within six days on a single machine. We also compare PDLP with Gurobi barrier, primal simplex, and dual simplex implementations. These traditional methods are designed to solve linear programs to much tighter optimality gaps but struggle to solve these instances. Gurobi barrier solves only three instances, exceeding our 1TB RAM limit on the other eight. While primal and dual simplex are more memory-efficient than the barrier method, they are slower and solve only three instances within six days. Compared with the conference version of this work (in: Advances in Neural Information Processing Systems 34 (NeurIPS 2021)), the key new contributions are: (i) feasibility polishing, a technique that quickly finds solutions that are approximately optimal but almost exactly feasible (without which only two of the eleven problems can be solved); (ii) a multithreaded C++ implementation available in Google OR-Tools; and (iii) a new collection of large-scale LP problems. Note that the conference version should be referred to for comparisons with SCS and ablation studies, which we do not repeat in this paper.

math.OC↗

arXiv2023

Probabilistic Inference in Reinforcement Learning Done Right

A popular perspective in Reinforcement learning (RL) casts the problem as probabilistic inference on a graphical model of the Markov decision process (MDP). The core object of study is the probability of each state-action pair being visited under the optimal policy. Previous approaches to approximate this quantity can be arbitrarily poor, leading to algorithms that do not implement genuine statistical inference and consequently do not perform well in challenging problems. In this work, we undertake a rigorous Bayesian treatment of the posterior probability of state-action optimality and clarify how it flows through the MDP. We first reveal that this quantity can indeed be used to generate a policy that explores efficiently, as measured by regret. Unfortunately, computing it is intractable, so we derive a new variational Bayesian approximation yielding a tractable convex optimization problem and establish that the resulting policy also explores efficiently. We call our approach VAPOR and show that it has strong connections to Thompson sampling, K-learning, and maximum entropy exploration. We conclude with some experiments demonstrating the performance advantage of a deep RL version of VAPOR.

cs.LG↗

arXiv2023

Efficient Exploration via Epistemic-Risk-Seeking Policy Optimization

Exploration remains a key challenge in deep reinforcement learning (RL). Optimism in the face of uncertainty is a well-known heuristic with theoretical guarantees in the tabular setting, but how best to translate the principle to deep reinforcement learning, which involves online stochastic gradients and deep network function approximators, is not fully understood. In this paper we propose a new, differentiable optimistic objective that when optimized yields a policy that provably explores efficiently, with guarantees even under function approximation. Our new objective is a zero-sum two-player game derived from endowing the agent with an epistemic-risk-seeking utility function, which converts uncertainty into value and encourages the agent to explore uncertain states. We show that the solution to this game minimizes an upper bound on the regret, with the 'players' each attempting to minimize one component of a particular regret decomposition. We derive a new model-free algorithm which we call 'epistemic-risk-seeking actor-critic' (ERSAC), which is simply an application of simultaneous stochastic gradient ascent-descent to the game. Finally, we discuss a recipe for incorporating off-policy data and show that combining the risk-seeking objective with replay data yields a double benefit in terms of statistical efficiency. We conclude with some results showing good performance of a deep RL agent using the technique on the challenging 'DeepSea' environment, showing significant performance improvements even over other efficient exploration techniques, as well as improved performance on the Atari benchmark.

cs.LG↗

arXiv2023

Reward is enough for convex MDPs

Maximising a cumulative reward function that is Markov and stationary, i.e., defined over state-action pairs and independent of time, is sufficient to capture many kinds of goals in a Markov decision process (MDP). However, not all goals can be captured in this manner. In this paper we study convex MDPs in which goals are expressed as convex functions of the stationary distribution and show that they cannot be formulated using stationary reward functions. Convex MDPs generalize the standard reinforcement learning (RL) problem formulation to a larger framework that includes many supervised and unsupervised RL problems, such as apprenticeship learning, constrained MDPs, and so-called `pure exploration'. Our approach is to reformulate the convex MDP problem as a min-max game involving policy and cost (negative reward) `players', using Fenchel duality. We propose a meta-algorithm for solving this problem and show that it unifies many existing algorithms in the literature.

cs.AI↗

arXiv2023

ReLOAD: Reinforcement Learning with Optimistic Ascent-Descent for Last-Iterate Convergence in Constrained MDPs

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

cs.LG↗

arXiv2023

Optimistic Meta-Gradients

We study the connection between gradient-based meta-learning and convex op-timisation. We observe that gradient descent with momentum is a special case of meta-gradients, and building on recent results in optimisation, we prove convergence rates for meta-learning in the single task setting. While a meta-learned update rule can yield faster convergence up to constant factor, it is not sufficient for acceleration. Instead, some form of optimism is required. We show that optimism in meta-learning can be captured through Bootstrapped Meta-Gradients (Flennerhag et al., 2022), providing deeper insight into its underlying mechanics.

cs.LG↗

arXiv2022

POMRL: No-Regret Learning-to-Plan with Increasing Horizons

We study the problem of planning under model uncertainty in an online meta-reinforcement learning (RL) setting where an agent is presented with a sequence of related tasks with limited interactions per task. The agent can use its experience in each task and across tasks to estimate both the transition model and the distribution over tasks. We propose an algorithm to meta-learn the underlying structure across tasks, utilize it to plan in each task, and upper-bound the regret of the planning loss. Our bound suggests that the average regret over tasks decreases as the number of tasks increases and as the tasks are more similar. In the classical single-task setting, it is known that the planning horizon should depend on the estimated model's accuracy, that is, on the number of samples within task. We generalize this finding to meta-RL and study this dependence of planning horizons on the number of tasks. Based on our theoretical findings, we derive heuristics for selecting slowly increasing discount factors, and we validate its significance empirically.

cs.AI↗

arXiv2022

Variational Bayesian Reinforcement Learning with Regret Bounds

In reinforcement learning the Q-values summarize the expected future rewards that the agent will attain. However, they cannot capture the epistemic uncertainty about those rewards. In this work we derive a new Bellman operator with associated fixed point we call the `knowledge values'. These K-values compress both the expected future rewards and the epistemic uncertainty into a single value, so that high uncertainty, high reward, or both, can yield high K-values. The key principle is to endow the agent with a risk-seeking utility function that is carefully tuned to balance exploration and exploitation. When the agent follows a Boltzmann policy over the K-values it yields a Bayes regret bound of $\tilde O(L \sqrt{S A T})$, where $L$ is the time horizon, $S$ is the total number of states, $A$ is the number of actions, and $T$ is the number of elapsed timesteps. We show deep connections of this approach to the soft-max and maximum-entropy strands of research in reinforcement learning.

cs.LG↗

arXiv2022

On the connection between Bregman divergence and value in regularized Markov decision processes

In this short note we derive a relationship between the Bregman divergence from the current policy to the optimal policy and the suboptimality of the current value function in a regularized Markov decision process. This result has implications for multi-task reinforcement learning, offline reinforcement learning, and regret analysis under function approximation, among others.

cs.LG↗

arXiv2022

The Neural Testbed: Evaluating Joint Predictions

Predictive distributions quantify uncertainties ignored by point estimates. This paper introduces The Neural Testbed: an open-source benchmark for controlled and principled evaluation of agents that generate such predictions. Crucially, the testbed assesses agents not only on the quality of their marginal predictions per input, but also on their joint predictions across many inputs. We evaluate a range of agents using a simple neural network data generating process. Our results indicate that some popular Bayesian deep learning agents do not fare well with joint predictions, even when they can produce accurate marginal predictions. We also show that the quality of joint predictions drives performance in downstream decision tasks. We find these results are robust across choice a wide range of generative models, and highlight the practical importance of joint predictions to the community.

cs.LG↗

arXiv2022

Practical Large-Scale Linear Programming using Primal-Dual Hybrid Gradient

We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core operation is matrix-vector multiplications. PDLP is derived by applying the primal-dual hybrid gradient (PDHG) method, popularized by Chambolle and Pock (2011), to a saddle-point formulation of LP. PDLP enhances PDHG for LP by combining several new techniques with older tricks from the literature; the enhancements include diagonal preconditioning, presolving, adaptive step sizes, and adaptive restarting. PDLP improves the state of the art for first-order methods applied to LP. We compare PDLP with SCS, an ADMM-based solver, on a set of 383 LP instances derived from MIPLIB 2017. With a target of $10^{-8}$ relative accuracy and 1 hour time limit, PDLP achieves a 6.3x reduction in the geometric mean of solve times and a 4.6x reduction in the number of instances unsolved (from 227 to 49). Furthermore, we highlight standard benchmark instances and a large-scale application (PageRank) where our open-source prototype of PDLP, written in Julia, outperforms a commercial LP solver.

math.OC↗

arXiv2022

Discovering Diverse Nearly Optimal Policies with Successor Features

Finding different solutions to the same problem is a key aspect of intelligence associated with creativity and adaptation to novel situations. In reinforcement learning, a set of diverse policies can be useful for exploration, transfer, hierarchy, and robustness. We propose Diverse Successive Policies, a method for discovering policies that are diverse in the space of Successor Features, while assuring that they are near optimal. We formalize the problem as a Constrained Markov Decision Process (CMDP) where the goal is to find policies that maximize diversity, characterized by an intrinsic diversity reward, while remaining near-optimal with respect to the extrinsic reward of the MDP. We also analyze how recently proposed robustness and discrimination rewards perform and find that they are sensitive to the initialization of the procedure and may converge to sub-optimal solutions. To alleviate this, we propose new explicit diversity rewards that aim to minimize the correlation between the Successor Features of the policies in the set. We compare the different diversity mechanisms in the DeepMind Control Suite and find that the type of explicit diversity we are proposing is important to discover distinct behavior, like for example different locomotion patterns.

cs.AI↗

arXiv2021

Discovering a set of policies for the worst case reward

We study the problem of how to construct a set of policies that can be composed together to solve a collection of reinforcement learning tasks. Each task is a different reward function defined as a linear combination of known features. We consider a specific class of policy compositions which we call set improving policies (SIPs): given a set of policies and a set of tasks, a SIP is any composition of the former whose performance is at least as good as that of its constituents across all the tasks. We focus on the most conservative instantiation of SIPs, set-max policies (SMPs), so our analysis extends to any SIP. This includes known policy-composition operators like generalized policy improvement. Our main contribution is a policy iteration algorithm that builds a set of policies in order to maximize the worst-case performance of the resulting SMP on the set of tasks. The algorithm works by successively adding new policies to the set. We show that the worst-case performance of the resulting SMP strictly improves at each iteration, and the algorithm only stops when there does not exist a policy that leads to improved performance. We empirically evaluate our algorithm on a grid world and also on a set of domains from the DeepMind control suite. We confirm our theoretical results regarding the monotonically improving performance of our algorithm. Interestingly, we also show empirically that the sets of policies computed by the algorithm are diverse, leading to different trajectories in the grid world and very distinct locomotion skills in the control suite.

cs.AI↗

arXiv2021

Variational Bayesian Optimistic Sampling

We consider online sequential decision problems where an agent must balance exploration and exploitation. We derive a set of Bayesian `optimistic' policies which, in the stochastic multi-armed bandit case, includes the Thompson sampling policy. We provide a new analysis showing that any algorithm producing policies in the optimistic set enjoys $\tilde O(\sqrt{AT})$ Bayesian regret for a problem with $A$ actions after $T$ rounds. We extend the regret analysis for optimistic policies to bilinear saddle-point problems which include zero-sum matrix games and constrained bandits as special cases. In this case we show that Thompson sampling can produce policies outside of the optimistic set and suffer linear regret in some instances. Finding a policy inside the optimistic set amounts to solving a convex optimization problem and we call the resulting algorithm `variational Bayesian optimistic sampling' (VBOS). The procedure works for any posteriors, \ie, it does not require the posterior to have any special properties, such as log-concavity, unimodality, or smoothness. The variational view of the problem has many useful properties, including the ability to tune the exploration-exploitation tradeoff, add regularization, incorporate constraints, and linearly parameterize the policy.

stat.ML↗

arXiv2021

Solving Mixed Integer Programs Using Neural Networks

Mixed Integer Programming (MIP) solvers rely on an array of sophisticated heuristics developed with decades of research to solve large-scale MIP instances encountered in practice. Machine learning offers to automatically construct better heuristics from data by exploiting shared structure among instances in the data. This paper applies learning to the two key sub-tasks of a MIP solver, generating a high-quality joint variable assignment, and bounding the gap in objective value between that assignment and an optimal one. Our approach constructs two corresponding neural network-based components, Neural Diving and Neural Branching, to use in a base MIP solver such as SCIP. Neural Diving learns a deep neural network to generate multiple partial assignments for its integer variables, and the resulting smaller MIPs for un-assigned variables are solved with SCIP to construct high quality joint assignments. Neural Branching learns a deep neural network to make variable selection decisions in branch-and-bound to bound the objective value gap with a small tree. This is done by imitating a new variant of Full Strong Branching we propose that scales to large instances using GPUs. We evaluate our approach on six diverse real-world datasets, including two Google production datasets and MIPLIB, by training separate neural networks on each. Most instances in all the datasets combined have $10^3-10^6$ variables and constraints after presolve, which is significantly larger than previous learning approaches. Comparing solvers with respect to primal-dual gap averaged over a held-out set of instances, the learning-augmented SCIP is 2x to 10x better on all datasets except one on which it is $10^5$x better, at large time limits. To the best of our knowledge, ours is the first learning approach to demonstrate such large improvements over SCIP on both large-scale real-world application datasets and MIPLIB.

math.OC↗

arXiv2021

Operator splitting for a homogeneous embedding of the linear complementarity problem

The linear complementarity problem (LCP) is a general set membership problem that includes quadratic cone programming as a special case. In this work we consider a homogeneous embedding of the LCP, which encodes both the optimality conditions of the original LCP as well as certificates of infeasibility. The resulting problem can be expressed as a monotone inclusion problem involving the sum of two maximal monotone operators, to which we apply Douglas-Rachford splitting. The resulting algorithm has almost identical per-iteration cost as applying the splitting to the LCP directly. Specifically, each iteration requires solving a linear system and projecting onto a convex cone. The resulting algorithm has no explicit hyper-parameters and is able to return a primal-dual solution should one exist or a certificate of infeasibility otherwise. If a sequence of related problems are solved it can easily be warm-started and make use of factorization caching of the linear system. We demonstrate on a range of public and synthetic datasets that for feasible problems our approach tends to be somewhat faster than applying operator splitting directly to the LCP, and in cases of infeasibility our approach can be significantly faster than alternative approaches based on diverging iterates. The algorithm we describe has been implemented in C and is available open-source as SCS-3.0.

math.OC↗