Training LLMs relies on distributed implementations using multiple GPUs to compute gradients in parallel with sharded optimizers. However, synchronizing gradients in data parallel setups introduces communication overhead that grows with the number of workers, limiting parallelization efficiency. Local optimization algorithms reduce communications but incur high memory costs as they prevent optimizer state sharding, hindering scalability. To address this, we propose $\textbf{AC}$cumulate while $\textbf{CO}$mmunicate ($\texttt{ACCO}$), a memory-efficient optimization algorithm for distributed LLM training. By synchronizing delayed gradients while computing new ones, $\texttt{ACCO}$ reduces GPU idle time and supports heterogeneous hardware. To mitigate the convergence issues caused by delayed updates, we introduce a novel technique ensuring training dynamics align with standard distributed optimization. Compared to ZeRO-1, our approach is significantly faster and scales effectively across heterogeneous hardware.

DADAO is the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of $L$-smooth and $\mu$-strongly convex functions distributed over a network of size $n$. Modeling the gradient updates and gossip communication procedures with separate independent Poisson Point Processes allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous. This leads to communication acceleration compared to synchronous approaches. Our method employs primal gradients and avoids using a multi-consensus inner loop and other ad-hoc mechanisms. By relating the smallest positive eigenvalue $1/\chi_1$ of the Laplacian matrix $\Lambda$ and the maximal resistance $\chi_2\leq \chi_1$ of the graph to a sufficient minimal communication rate, we show that DADAO requires $\mathcal{O}(n\sqrt{\frac{L}{\mu}}\log(\frac{1}{\epsilon}))$ local gradients and only $\mathcal{O}(\sqrt{\chi_1\chi_2}\operatorname{Tr}\Lambda\sqrt{\frac{L}{\mu}}\log(\frac{1}{\epsilon}))$ communications to reach $\epsilon$-precision, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method. Moreover, we propose a SDP relaxation to find the gossip rate of each edge minimizing the total number of communications for a given graph, resulting in faster convergence compared to standard approaches relying on uniform communication weights.

This work introduces DADAO: the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of $L$-smooth and $\mu$-strongly convex functions distributed over a given network of size $n$. Our key insight is based on modeling the local gradient updates and gossip communication procedures with separate independent Poisson Point Processes. This allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous. This leads to communication acceleration compared to synchronous approaches. Our new method employs primal gradients and does not use a multi-consensus inner loop nor other ad-hoc mechanisms such as Error Feedback, Gradient Tracking, or a Proximal operator. By relating the inverse of the smallest positive eigenvalue of the Laplacian matrix $\chi_1$ and the maximal resistance $\chi_2\leq \chi_1$ of the graph to a sufficient minimal communication rate between the nodes of the network, we show that our algorithm requires $\mathcal{O}(n\sqrt{\frac{L}{\mu}}\log(\frac{1}{\epsilon}))$ local gradients and only $\mathcal{O}(n\sqrt{\chi_1\chi_2}\sqrt{\frac{L}{\mu}}\log(\frac{1}{\epsilon}))$ communications to reach a precision $\epsilon$, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for both computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method.

International audience

Learning heuristics for combinatorial optimization problems through graph neural networks have recently shown promising results on some classic NP-hard problems. These are single-level optimization problems with only one player. Multilevel combinatorial optimization problems are their generalization, encompassing situations with multiple players taking decisions sequentially. By framing them in a multi-agent reinforcement learning setting, we devise a value-based method to learn to solve multilevel budgeted combinatorial problems involving two players in a zero-sum game over a graph. Our framework is based on a simple curriculum: if an agent knows how to estimate the value of instances with budgets up to $B$, then solving instances with budget $B+1$ can be done in polynomial time regardless of the direction of the optimization by checking the value of every possible afterstate. Thus, in a bottom-up approach, we generate datasets of heuristically solved instances with increasingly larger budgets to train our agent. We report results close to optimality on graphs up to $100$ nodes and a $185 \times$ speedup on average compared to the quickest exact solver known for the Multilevel Critical Node problem, a max-min-max trilevel problem that has been shown to be at least $\Sigma_2^p$-hard.