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Title: Reinforced Genetic Algorithm Learning for Optimizing Computation Graphs

Paper content:
We present a deep reinforcement learning approach to minimizing the execution cost of neural network computation graphs in an optimizing compiler.
Unlike earlier learning-based works that require training the optimizer on the same graph to be optimized, we propose a learning approach that trains an optimizer offline and then generalizes to previously unseen graphs without further training.
This allows our approach to produce high-quality execution decisions on real-world TensorFlow graphs in seconds instead of hours.
We consider two optimization tasks for computation graphs: minimizing running time and peak memory usage.
In comparison to an extensive set of baselines, our approach achieves significant improvements over classical and other learning-based methods on these two tasks.
Deep Learning frameworks such as MXNet (Chen et al., 2015) , PyTorch (Paszke et al., 2017) , and TensorFlow (TensorFlow Authors, 2016a) represent neural network models as computation graphs.
Efficiently executing such graphs requires optimizing discrete decisions about how to map the computations in a graph onto hardware so as to minimize a relevant cost metric (e.g., running time, peak memory).
Given that execution efficiency is critical for the success of neural networks, there is growing interest in the use of optimizing static compilers for neural network computation graphs, such as Glow (Rotem et al., 2018) , MLIR (MLIR Authors, 2018) , TVM (Chen et al., 2018a) , and XLA (XLA team, 2017 ).
Here we consider the model parallelism setting where a computation graph can be executed using multiple devices in parallel.
Nodes of the graph are computational tasks, and directed edges denote dependencies between them.
We consider here jointly optimizing over placement, i.e., which nodes are executed on which devices, and schedule, i.e., the node execution order on each device.
These decisions are typically made in either one or two passes in the compiler.
We consider two different objectives:
1) minimize running time, subject to not exceeding device memory limits, and
2) minimize peak memory usage.
In the optimization literature, such problems are studied under the class of task scheduling, which is known to be NP-hard in typical settings (Sinnen, 2007; Kwok & Ahmad, 1999) .
As scheduling and placement are just a few of the many complex decisions made in a compiler, it is essential in a production setting that a solution
1) produce solutions of acceptable quality fast, even on large graphs (e.g., thousands of nodes) and decision spaces, and
2) handle diverse graphs from various types of applications, neural network architectures, and users.
In this work we consider learning an optimizer that satisfies these requirements.
Crucially, we aim to learn an optimizer that generalizes to a broad set of previously unseen computation graphs, without the need for training on such graphs, thus allowing it to be fast at test time.
Previous works on learning to optimize model parallelism decisions (Mirhoseini et al., 2017; Addanki et al., 2019) have not considered generalization to a broad set of graphs nor joint optimization of placement and scheduling.
In Mirhoseini et al. (2017; , learning is done from scratch for each computation graph and for placement decisions only, requiring hours (e.g., 12 to 27 hours per graph).
This is too slow to be broadly useful in a general-purpose production compiler.
We propose an approach that takes only seconds to optimize similar graphs.
In concurrent work to ours, Addanki et al. (2019) shows generalization to unseen graphs, but they are generated artificially by architecture search for a single learning task and dataset.
In contrast, we collect real user-defined graphs spanning a broad set of tasks, architectures, and datasets.
In addition, both Mirhoseini et al. (2017; and Fig. 1 : Overview of our approach.
The Biased Random Key Genetic Algorithm (BRKGA) is used to optimize execution decisions for a computation graph (e.g., placement and scheduling of nodes) with respect to a cost metric (e.g., running time, peak memory) computed using the performance model.
BRKGA requires proposal distributions for each node in the graph to generate candidate solutions in its search loop.
The default choice is agnostic to the input graph: uniform distribution over [0, 1] at all nodes.
We use a graph neural network policy to predict node-specific non-uniform proposal distribution choices (parameterized as beta distributions over [0, 1] ).
BRKGA is then run with those choices and outputs the best solution found by its iteration limit.
By controlling the non-uniformity of the distributions, the policy directs how BRKGA's search effort is allocated such that a better solution can be found with the same search budget.
Addanki et al. (2019) consider only placement decisions and rely on TensorFlow's dynamic scheduler; they do not address the static compiler setting where it is natural to jointly optimize scheduling and placement.
The key idea of our approach (Figure 1 ) is to learn a neural network that, conditioned on the input graph to be optimized, directs an existing optimization algorithm's search such that it finds a better solution in the same search budget.
We choose the Biased Random-Key Genetic Algorithm (BRKGA (Gonçalves & Resende, 2011) ) as the optimization algorithm after an extensive evaluation of several choices showed that it gives by far the best speed-vs-quality trade-off for our application.
BRKGA produces good solutions in just a few seconds even for real-world TensorFlow graphs with thousands of nodes, and we use learning to improve the solution quality significantly at similar speed.
We train a graph neural network (Battaglia et al., 2018) to take a computation graph as input and output node-specific proposal distributions to use in the mutant generation step of BRKGA's inner loop.
BRKGA is then run to completion with those input-dependent distribution choices, instead of inputagnostic default choices, to compute execution decisions.
The distributions are predicted at each node, resulting in a high-dimensional prediction problem.
There is no explicit supervision available, so we use the objective value as a reward signal in a contextual bandit approach with REINFORCE (Williams, 1992) .
Our approach, "Reinforced Genetic Algorithm Learning" (REGAL), uses the network's ability to generalize to new graphs to significantly improve the solution quality of the genetic algorithm for the same objective evaluation budget.
We follow the static compiler approach of constructing a coarse static cost model to evaluate execution decisions and optimizing them with respect to it, as done in (Addanki et al., 2018; Jia et al., 2018) .
This is in contrast to evaluating the cost by executing the computation graph on hardware (Mirhoseini et al., 2017; .
A computationally cheap cost model enables fast optimization.
It is also better suited for distributed training of RL policies since a cost model is cheap to replicate in parallel actors, while hardware environments are not.
Our cost model corresponds to classical NP-hard scheduling problems, so optimizing it is difficult.
In this paper we focus fully on learning to optimize this cost model, leaving integration with a compiler for future work.
We structure the neural network's task as predicting proposal distributions to use in the search over execution decisions, rather than the decisions themselves directly.
Empirically we have found the direct prediction approach to be too slow at inference time for our application and generalizes poorly.
Our approach potentially allows the network to learn a more abstract policy not directly tied to detailed decisions that are specific to particular graphs, which may generalize better to new graphs.
It can also make the learning task easier as the search may succeed even with sub-optimal proposal distribution predictions, thus smoothening the reward function and allowing the network to incrementally learn better proposals.
The node-specific proposal distribution choices provide a rich set of knobs for the network to flexibly direct the search.
Combining learning with a search algorithm has been shown to be successful (e.g., (Silver et al., 2017; ), and our work can be seen as an instance of the same high-level idea.
This paper makes several contributions:
• We are the first to demonstrate learning a policy for jointly optimizing placement and scheduling that generalizes to a broad set of real-world TensorFlow graphs.
REGAL significantly outperforms all baseline algorithms on two separate tasks of minimizing runtime and peak memory usage (section 5.3) on datasets constructed from 372 unique real-world TensorFlow graphs, the largest dataset of its kind in the literature and at least an order of magnitude larger than the ones in previous works (Mirhoseini et al., 2017; Chen et al., 2018b; Addanki et al., 2018; .
• We use a graph neural network to predict mutant sampling distributions of a genetic algorithm, specifically BRKGA, for the input graph to be optimized.
This directs BRKGA's search in an input-dependent way, improving solution quality for the same search budget.
• We compare extensively to classical optimization algorithms, such as enumerative search, local search, genetic search, and other heuristics, and analyze room-for-improvement in the objective value available to be captured via learning.
Both are missing in previous works.
By training a graph neural network policy to predict graph-conditional node-level distributions for BRKGA, REGAL successfully generalizes to new graphs, significantly outperforms all baselines in solution quality, and computes solutions in about one second on average per TensorFlow test set graph.
REGAL's speed and generalization make it a strong choice for use in a production compiler that needs to handle a diverse set of graphs under a limited time budget.
We foresee several extensions.
Integrating REGAL into a neural network compiler would allow us to evaluate the end-to-end gains due to better placement and scheduling decisions.
To further improve REGAL's own performance, one could use a Mixture of Experts architecture.
Given the diversity of graphs, a mixture model can train specialized sub-models on different types of graphs (e.g., convolutional networks, recurrent networks, etc.).
Another is to replace BRKGA with alternatives, e.g., combining learned neural policies with local search.
figure 6 give statistics for the number of nodes and edges in the datasets.
The broad range of graph sizes indicates the diversity of the datasets.

assistant: text: We use deep RL to learn a policy that directs the search of a genetic algorithm to better optimize the execution cost of computation graphs, and show improved results on real-world TensorFlow graphs.