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Learning Rate Schedule Piecewise Constant Decay A

Leo Migdal
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learning rate schedule piecewise constant decay a

A LearningRateSchedule that uses a piecewise constant decay schedule. The function returns a 1-arg callable to compute the piecewise constant when passed the current optimizer step. This can be useful for changing the learning rate value across different invocations of optimizer functions. use a learning rate that's 1.0 for the first 100001 steps, 0.5 for the next 10000 steps, and 0.1 for any additional steps. You can pass this schedule directly into a keras.optimizers.Optimizer as the learning rate. The learning rate schedule is also serializable and deserializable using keras.optimizers.schedules.serialize and keras.optimizers.schedules.deserialize.

A 1-arg callable learning rate schedule that takes the current optimizer step and outputs the decayed learning rate, a scalar tensor of the same type as the boundary tensors. A LearningRateSchedule that uses a piecewise constant decay schedule The function returns a 1-arg callable to compute the piecewise constant when passed the current optimizer step. This can be useful for changing the learning rate value across different invocations of optimizer functions. Example: use a learning rate that’s 1.0 for the first 100001 steps, 0.5 for the next 10000 steps, and 0.1 for any additional steps. ```

boundaries <- as.integer(c(100000, 110000)) learning_rate_fn <- learning_rate_schedule_piecewise_constant_decay( ``You can pass this schedule directly into a keras Optimizer as thelearning_rate`. A LearningRateSchedule that uses a piecewise constant decay schedule. The function returns a 1-arg callable to compute the piecewise constant when passed the current optimizer step. This can be useful for changing the learning rate value across different invocations of optimizer functions.

Example: use a learning rate that's 1.0 for the first 100001 steps, 0.5 for the next 10000 steps, and 0.1 for any additional steps. You can pass this schedule directly into a keras.optimizers.Optimizer as the learning rate. The learning rate schedule is also serializable and deserializable using keras.optimizers.schedules.serialize and keras.optimizers.schedules.deserialize. The output of the 1-arg function that takes the step is values[0] when step <= boundaries[0], values[1] when step > boundaries[0] and step <= boundaries[1], ..., and values[-1] when step > boundaries[-1]. So far we primarily focused on optimization algorithms for how to update the weight vectors rather than on the rate at which they are being updated. Nonetheless, adjusting the learning rate is often just as important as the actual algorithm.

There are a number of aspects to consider: Most obviously the magnitude of the learning rate matters. If it is too large, optimization diverges, if it is too small, it takes too long to train or we end up with a suboptimal result. We saw previously that the condition number of the problem matters (see e.g., Section 12.6 for details). Intuitively it is the ratio of the amount of change in the least sensitive direction vs. the most sensitive one.

Secondly, the rate of decay is just as important. If the learning rate remains large we may simply end up bouncing around the minimum and thus not reach optimality. Section 12.5 discussed this in some detail and we analyzed performance guarantees in Section 12.4. In short, we want the rate to decay, but probably more slowly than \(\mathcal{O}(t^{-\frac{1}{2}})\) which would be a good choice for convex problems. Another aspect that is equally important is initialization. This pertains both to how the parameters are set initially (review Section 5.4 for details) and also how they evolve initially.

This goes under the moniker of warmup, i.e., how rapidly we start moving towards the solution initially. Large steps in the beginning might not be beneficial, in particular since the initial set of parameters is random. The initial update directions might be quite meaningless, too. Lastly, there are a number of optimization variants that perform cyclical learning rate adjustment. This is beyond the scope of the current chapter. We recommend the reader to review details in Izmailov et al.

(2018), e.g., how to obtain better solutions by averaging over an entire path of parameters. A LearningRateSchedule that uses a piecewise constant decay schedule A list of Tensors or R numerics with strictly increasing entries, and with all elements having the same type as the optimizer step. A list of Tensors or R numerics that specifies the values for the intervals defined by boundaries. It should have one more element than boundaries, and all elements should have the same type. For backwards and forwards compatibility

A string. Optional name of the operation. Defaults to 'PiecewiseConstant'. A LearningRateSchedule that uses a piecewise constant decay schedule. The function returns a 1-arg callable to compute the piecewise constant when passed the current optimizer step. This can be useful for changing the learning rate value across different invocations of optimizer functions.

Example: use a learning rate that's 1.0 for the first 100001 steps, 0.5 for the next 10000 steps, and 0.1 for any additional steps. You can pass this schedule directly into a keras.optimizers.Optimizer as the learning rate. The learning rate schedule is also serializable and deserializable using keras.optimizers.schedules.serialize and keras.optimizers.schedules.deserialize. The output of the 1-arg function that takes the step is values[0] when step <= boundaries[0], values[1] when step > boundaries[0] and step <= boundaries[1], ..., and values[-1] when step > boundaries[-1]. Finding a good learning rate is important. Another way use learning schudule (specific to tf.keras):

Define the learning rate using one of the schedules available in keras.optimizers.schedules and then pass this learning rate to any optimizer. View source: R/learning_rate_schedules.R A LearningRateSchedule that uses a piecewise constant decay schedule A list of Tensors or R numerics with strictly increasing entries, and with all elements having the same type as the optimizer step. A list of Tensors or R numerics that specifies the values for the intervals defined by boundaries. It should have one more element than boundaries, and all elements should have the same type.

For backwards and forwards compatibility A LearningRateSchedule that uses a piecewise constant decay schedule. The function returns a 1-arg callable to compute the piecewise constant when passed the current optimizer step. This can be useful for changing the learning rate value across different invocations of optimizer functions. use a learning rate that's 1.0 for the first 100001 steps, 0.5 for the next 10000 steps, and 0.1 for any additional steps. You can pass this schedule directly into a tf.keras.optimizers.Optimizer as the learning rate.

The learning rate schedule is also serializable and deserializable using tf.keras.optimizers.schedules.serialize and tf.keras.optimizers.schedules.deserialize. A 1-arg callable learning rate schedule that takes the current optimizer step and outputs the decayed learning rate, a scalar Tensor of the same type as the boundary tensors.

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There are a number of aspects to consider: Most obviously the magnitude of the learning rate matters. If it is too large, optimization diverges, if it is too small, it takes too long to train or we end up with a suboptimal result. We saw previously that the condition number of the problem matters (see e.g., Section 12.6 for details). Intuitively it is the ratio of the amount of change in the least...