Is learning rate decay a regularization technique?

Sahil_malik: <p>Upto my understanding, it is a regularization technique, because it helps to learn model correctly and in generalization. But I am still confused at whether it would be correct or not to call it a “regularization” method.??</p>
<p>Thank you!</p>

KFrank: <p>Hi Sahil!</p>
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<img loading="lazy" alt="" width="24" height="24" src="https://discuss.pytorch.org/letter_avatar_proxy/v4/letter/s/a183cd/48.png" class="avatar"> Sahil_malik:</div>
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<p>would be correct or not to call it a “regularization” method.??</p>
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<p>I would not call learning-rate decay <em>regularization.</em></p>
<p>Of course, we’re discussing semantics – the meaning of the term<br>
“regularization.”  But I think it has a fairly standard definition – or at<br>
least connotation – in this context.</p>
<p>We have a loss function as a function of parameter space, and an<br>
optimization algorithm that seeks to move around in parameter space<br>
to locations with lower losses.  (In practice, with neural networks, we<br>
neither find the global minimum, nor even a local minimum.  We just<br>
want to find a “good enough” location in parameter space with a “low<br>
enough” value of the loss.)</p>
<p>Learning-rate decay is just part of the optimization algorithm, just as<br>
is, say, adding momentum to gradient descent or fancier things like<br>
adaptive momentum.  These don’t change where in parameter space<br>
you want to go – they just try to get you there faster.</p>
<p><em>Regularization,</em> however, changes the loss function so that different<br>
regions of parameter space are favored.  For example, <em>weight decay,</em><br>
which we often think of as being part of the optimization algorithm, is<br>
essentially equivalent to adding an L2 regularizer to the loss function.<br>
This means we prefer weights that are smaller, even if they would lead<br>
to a (modestly) larger unregularized loss.  This can be used to prevent<br>
weights from becoming very large and producing numerical instability.<br>
It can also lead to weights that generalize better.  But, to emphasize,<br>
it changes which points in parameter space are favored (by the<br>
regularized loss) relative to other points.</p>
<p>Similarly, one can add sparsity penalties (e.g., L1 regularizers) to the<br>
loss function to prefer having more parameters that are close to zero.<br>
Again, in many instances, such sparser parameter sets generalize<br>
better, <em>even though</em> they have larger unregularized losses computed<br>
for the training data.</p>
<p>To summarize:  Regularization modifies the loss, changing which regions<br>
of parameter space are favored, while things like learning-rate decay<br>
modify the optimization algorithm so that it moves you to the favored<br>
regions of parameter space more efficiently.</p>
<p>Best.</p>
<p>K. Frank</p>

Sahil_malik: <p>Thank you so much for your valuable feedback.</p>
<p>Would you consider then LRReduceOnPlateau and EarlyStopping as regularization as this blog “<a href="https://maelfabien.github.io/deeplearning/regu/#overfitting" class="inline-onebox" rel="noopener nofollow ugc">Prevent Overfitting of Neural Networks -</a>” is doing?</p>
<p>Thank you!</p>

KFrank: <p>Hi Sahil!</p>
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<img loading="lazy" alt="" width="24" height="24" src="https://discuss.pytorch.org/letter_avatar_proxy/v4/letter/s/a183cd/48.png" class="avatar"> Sahil_malik:</div>
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<p>Would you consider then LRReduceOnPlateau and EarlyStopping as regularization</p>
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<p>Again, it’s a question of semantics, but I would not call techniques such<br>
as early stopping and the algorithm in pytorch’s <code>ReduceLROnPlateau</code><br>
kinds of regularization.  They are overlays on top of the optimization<br>
algorithm that take a peek at some validation results.  But they don’t<br>
in any substantive sense affect the regions in parameter towards which<br>
the optimization algorithm moves you.</p>
<p>That is, in my language, the weights in the network are not being in<br>
any way regularized.</p>
<p>Regularization can be used to reduce overfitting, but I would not say<br>
that anything that reduces overfitting is regularization.  For example,<br>
training on more data (or sometimes on augmented data) will reduce<br>
overfitting (and will move you towards different regions of parameter<br>
space), but I would not call training on more data “regularization.”</p>
<p>Best.</p>
<p>K. Frank</p>