First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This theoretical paper derives low bounds on the number of samples needed to learn graphs (and not factors) from data. The paper uses various versions of the Fano lemma, e.g. Derivations and arguments are purely information-theoretic. The results are probably correct (I did not check the algebra), however I am not sure about the value of what is reported.

Causal Bayesian Optimization (CBO) is a methodology designed to optimize an outcome variable by leveraging known causal relationships through targeted interventions. Traditional CBO methods require a fully and accurately specified causal graph, which is a limitation in many real-world scenarios where such graphs are unknown. To address this, we propose a new method for the CBO framework that operates without prior knowledge of the causal graph. Consistent with causal bandit theory, we demonstrate through theoretical analysis and that focusing on the direct causal parents of the target variable is sufficient for optimization, and provide empirical validation in the context of CBO. Furthermore we introduce a new method that learns a Bayesian posterior over the direct parents of the target variable. This allows us to optimize the outcome variable while simultaneously learning the causal structure. Our contributions include a derivation of the closed-form posterior distribution for the linear case. In the nonlinear case where the posterior is not tractable, we present a Gaussian Process (GP) approximation that still enables CBO by inferring the parents of the outcome variable. The proposed method performs competitively with existing benchmarks and scales well to larger graphs, making it a practical tool for real-world applications where causal information is incomplete.

A common technique to improve speed and robustness of learning in deep reinforcement learning (DRL) and many other machine learning algorithms is to run multiple learning agents in parallel. A neglected component in the development of these algorithms has been how best to arrange the learning agents involved to better facilitate distributed search. Here we draw upon results from the networked optimization and collective intelligence literatures suggesting that arranging learning agents in less than fully connected topologies (the implicit way agents are commonly arranged in) can improve learning. We explore the relative performance of four popular families of graphs and observe that one such family (Erdos-Renyi random graphs) empirically outperforms the standard fully-connected communication topology across several DRL benchmark tasks. We observe that 1000 learning agents arranged in an Erdos-Renyi graph can perform as well as 3000 agents arranged in the standard fully-connected topology, showing the large learning improvement possible when carefully designing the topology over which agents communicate. We complement these empirical results with a preliminary theoretical investigation of why less than fully connected topologies can perform better. Overall, our work suggests that distributed machine learning algorithms could be made more efficient if the communication topology between learning agents was optimized.

In this empirical paper, we investigate how learning agents can be arranged in more efficient communication topologies for improved learning. This is an important problem because a common technique to improve speed and robustness of learning in deep reinforcement learning and many other machine learning algorithms is to run multiple learning agents in parallel. The standard communication architecture typically involves all agents intermittently communicating with each other (fully connected topology) or with a centralized server (star topology). Unfortunately, optimizing the topology of communication over the space of all possible graphs is a hard problem, so we borrow results from the networked optimization and collective intelligence literatures which suggest that certain families of network topologies can lead to strong improvements over fully-connected networks. We start by introducing alternative network topologies to DRL benchmark tasks under the Evolution Strategies paradigm which we call Network Evolution Strategies. We explore the relative performance of the four main graph families and observe that one such family (Erdos-Renyi random graphs) empirically outperforms all other families, including the de facto fully-connected communication topologies. Additionally, the use of alternative network topologies has a multiplicative performance effect: we observe that when 1000 learning agents are arranged in a carefully designed communication topology, they can compete with 3000 agents arranged in the de facto fully-connected topology. Overall, our work suggests that distributed machine learning algorithms would learn more efficiently if the communication topology between learning agents was optimized.