• Corpus ID: 235826177

Unbiased Gradient Estimation in Unrolled Computation Graphs with Persistent Evolution Strategies

@article{Vicol2021UnbiasedGE,
  title={Unbiased Gradient Estimation in Unrolled Computation Graphs with Persistent Evolution Strategies},
  author={Paul Vicol and Luke Metz and Jascha Sohl-Dickstein},
  journal={ArXiv},
  year={2021},
  volume={abs/2112.13835}
}
Unrolled computation graphs arise in many scenarios, including training RNNs, tuning hyperparameters through unrolled optimization, and training learned optimizers. Current approaches to optimizing parameters in such computation graphs suffer from high variance gradients, bias, slow updates, or large memory usage. We introduce a method called Persistent Evolution Strategies (PES), which divides the computation graph into a series of truncated unrolls, and performs an evolution strategies-based… 

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References

SHOWING 1-10 OF 67 REFERENCES
Non-greedy Gradient-based Hyperparameter Optimization Over Long Horizons
TLDR
This work enables non-greediness over long horizons with a two-fold solution that derives a forward-mode differentiation algorithm for the popular momentum-based SGD optimizer, which allows for a memory cost that is constant with horizon size.
Forward and Reverse Gradient-Based Hyperparameter Optimization
We study two procedures (reverse-mode and forward-mode) for computing the gradient of the validation error with respect to the hyperparameters of any iterative learning algorithm such as stochastic
Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization
TLDR
A novel algorithm is introduced, Hyperband, for hyperparameter optimization as a pure-exploration non-stochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations.
Variance Reduction for Evolution Strategies via Structured Control Variates
TLDR
A new method for improving accuracy of the ES algorithms, that as opposed to recent approaches utilizing only Monte Carlo structure of the gradient estimator, takes advantage of the underlying MDP structure to reduce the variance.
Efficient Optimization of Loops and Limits with Randomized Telescoping Sums
TLDR
This work proposes randomized telescope (RT) gradient estimators, which represent the objective as the sum of a telescoping series and sample linear combinations of terms to provide cheap unbiased gradient estimates and derives a method for tuning RT estimators online to maximize a lower bound on the expected decrease in loss per unit of computation.
Unbiased Online Recurrent Optimization
TLDR
The novel Unbiased Online Recurrent Optimization (UORO) algorithm allows for online learning of general recurrent computational graphs such as recurrent network models and performs well thanks to the unbiasedness of its gradients.
Gradient-based Hyperparameter Optimization through Reversible Learning
TLDR
This work computes exact gradients of cross-validation performance with respect to all hyperparameters by chaining derivatives backwards through the entire training procedure, which allows us to optimize thousands ofhyperparameters, including step-size and momentum schedules, weight initialization distributions, richly parameterized regularization schemes, and neural network architectures.
Understanding Short-Horizon Bias in Stochastic Meta-Optimization
TLDR
Short-horizon bias is a fundamental problem that needs to be addressed if meta-optimization is to scale to practical neural net training regimes, and is introduced as a toy problem, a noisy quadratic cost function, on which it is analyzed.
On the Variance of Unbiased Online Recurrent Optimization
TLDR
The variance of the gradient estimate computed by UORO is analyzed, several possible changes to the method which reduce this variance are proposed, and a fundamental connection between its gradient estimate and the one that would be computed by REINFORCE if small amounts of noise were added to the RNN's hidden units is demonstrated.
Truncated Back-propagation for Bilevel Optimization
TLDR
It is found that optimization with the approximate gradient computed using few-step back-propagation often performs comparably to optimized with the exact gradient, while requiring far less memory and half the computation time.
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