I am using the ScipyOptimizerInterface in tensorflow. I provide a minimal example below, where I optimize function f(x)=p*x**2+x for some placeholder p.
Now, I would like to gradually change the value of the placeholder during optimization, i.e. I want to change p in every step of the optimizer. Because I am using ScipyOptimizerInterface however, I only get the final result of the optimization, not after a single step.
Question: How can I gradually change p over time? Of course, I still want the optimization to run efficiently.
Motivation
In my actual use case, I want the final result of my optimization to satisfy some non-linear constraints. To ensure this, I introduce a penalty for violations of those constraints, and weight this penalty with p. By increasing p over time, I allow some violations initially, but ensure that in the end, the constraints are satisfied.
Minimal example
import tensorflow as tf
from tensorflow.contrib.opt import ScipyOptimizerInterface
# setup variables
x=tf.get_variable("x",initializer=[1.0])
p=tf.placeholder(dtype=tf.float32)
val=10.0
# setup optimization
f=p*x**2+x
optimizer = ScipyOptimizerInterface(f, options={'maxiter': 100})
# run
with tf.Session() as session:
init = tf.global_variables_initializer()
session.run(init, feed_dict={p:val})
optimizer.minimize(session, feed_dict={p:val})
ret=session.run(x)
print(ret)
If it matters: My tensorflow version is 1.4.1.
Related
I have been trying to implement this paper . Basically what I want to do is sum the per client loss and compare the same with previous epoch. Then for each constituent layer of the model compare the KL divergence between the weights of the server and the client model to get the layer specific parameter updates and then doing a softmax and to decide whether an adaptive update or a normal FedAvg approach is needed.
The algorithm is as follows-
FedMed
I tried to make use of the code here to build a custom federated avg process. I got the basic understanding that there are some tf.computations and some tff.computations which are involved. I get that I need to make changes in the orchestration logic in the run_one_round function and basically manipulate the client outputs to do adaptive averaging instead of the vanilla federated averaging. The client_update tf.computation function basically returns all the values that I need i.e the weights_delta (can be used for client based model weights), model_output(which can be used to calculate the loss).
But I am not sure where exactly I should make the changes.
#tff.federated_computation(federated_server_state_type,
federated_dataset_type)
def run_one_round(server_state, federated_dataset):
server_message = tff.federated_map(server_message_fn, server_state)
server_message_at_client = tff.federated_broadcast(server_message)
client_outputs = tff.federated_map(
client_update_fn, (federated_dataset, server_message_at_client))
weight_denom = client_outputs.client_weight
# todo
# instead of using tff.federated_mean I wish to do a adaptive aggregation based on the client_outputs.weights_delta and server_state model
round_model_delta = tff.federated_mean(
client_outputs.weights_delta, weight=weight_denom)
#client_outputs.weights_delta has all the client model weights.
#client_outputs.client_weight has the number of examples per client.
#client_outputs.model_output has the output of the model per client example.
I want to make use of the server model weights using server_state object.
I want to calculate the KL divergence between the weights of server model and each client's model per layer. Then use a relative weight to aggregate the client weights instead of vanilla federated averaging.
Instead of using tff.federated_mean I wish to use a different strategy basically an adaptive one based on the algorithm above.
So I needed some suggestions on how to go about implementing this.
Basically what I want to do is :
1)Sum all the values of client losses.
2)Calculate the KL divergence per layerbasis of all the clients with server and then determine whether to use adaptive optimization or FedAvg.
Also is there a way to manipulate this value as a python value which will be helpful for debugging purposes( I tried to use tf.print but that was not helpful either). Thanks!
Simplest option: compute weights for mean on clients
If I read the algorithm above correctly, we need only compute some weights for a mean on-the-fly. tff.federated_mean accepts an optional CLIENTS-placed weight argument, so probably the simplest option here is to compute the desired weights on the clients and pass them in to the mean.
This would look something like (assuming the appropriate definitions of the variables used below, which we will comment on):
#tff.federated_computation(...)
def round_function(...):
...
# We assume there is a tff.Computation training_fn that performs training,
# and we're calling it here on the correct arguments
trained_clients = tff.federated_map(training_fn, clients_placed_arguments)
# Next we assume there is a variable in-scope server_model,
# representing the 'current global model'.
global_model_at_clients = tff.federated_broadcast(server_model)
# Here we assume a function compute_kl_divergence, which takes
# two structures of tensors and computes the KL divergence
# (as a scalar) between them. The two arguments here are clients-placed,
# so the result will be as well.
kl_div_at_clients = tff.federated_map(compute_kl_divergence,
(global_model_at_clients, trained_clients))
# Perhaps we wish to not use raw KL divergence as the weight, but rather
# some function thereof; if so, we map a postprocessing function to
# the computed divergences. The result will still be clients-placed.
mean_weight = tff.federated_map(postprocess_divergence, kl_div_at_clients)
# Now we simply use the computed weights in the mean.
return tff.federated_mean(trained_clients, weight=mean_weight)
More flexible tool: tff.federated_reduce
TFF generally encourages algorithm developers to implement whatever they can 'in the aggregation', and as such exposes some highly customizable primitives like tff.federated_reduce, which allow you to run arbitrary TensorFlow "in the stream" between clients and server. If the above reading of the desired algorithm is incorrect and something more involved is needed, or you wish to flexibly experiment with totally different notions of aggregation (something TFF encourages and is designed to support), this may be the option for you.
In TFF's heuristic typing language, tff.federated_reduce has signature:
<{T}#CLIENTS, U, (<U, T> -> U)> -> U#SERVER
Meaning, federated_reduce take a value of type T placed at the clients, a 'zero' in a reduction algebra of type U, and a function accepting a U and a T and producing a U, and applies this function 'in the stream' on the way between clients and server, producing a U placed at the server. The function (<U, T> -> U) will be applied to the partially accumulated value U, and the 'next' element in the stream T (note however that TFF does not guarantee ordering of these values), returning another partially accumulated value U. The 'zero' should represent whatever 'partially accumulated' means over the empty set in your application; this will be the starting point of the reduction.
Application to this problem
The components
Your reduction function needs access to two pieces of data: the global model state and the result of training on a given client. This maps quite nicely to the type T. In this application, we will have something like:
T = <server_model=server_model_type, trained_model=trained_model_type>
These two types are likely to be the same, but may not necessarily be so.
Your reduction function will accept the partial aggregate, your server model and your client-trained model, returning a new partial aggregate. Here we will start assuming the same reading of the algorithm as above, that of a weighted mean with particular weights. Generally, the easiest way to compute a mean is to keep two accumulators, one for numerator and one for denominator. This will affect the choice of zero and reduction function below.
Your zero should contain a structure of tensors with value 0 mapping to the weights of your model--this will be the numerator. This would be generated for you if you had an aggregation like tff.federated_sum (as TFF knows what the zero should be), but for this case you'll have to get your hands on such a tensor yourself. This shouldn't be too hard with tf.nest.map_structure and tf.zeros_like.
For the denominator, we will assume we just need a scalar. TFF and TF are much more flexible than this--you could keep a per-layer or per-parameter denominator if desired--but for simplicity we will assume that we just want to divide by a single float in the end.
Therefore our type U will be something like:
U = <numerator=server_model_type, denominator=tf.float32>
Finally we come to our reduction function. It will be more or less a different composition of the same pieces above; we will make slightly tighter assumptions about them here (in particular, that all the local functions are tff.tf_computations--a technical assumption, arguably a bug on TFF). Our reduction function will be along the lines (assuming appropriate type aliases):
#tff.tf_computation(U, T)
def reduction(partial_accumulate, next_element):
kl_div = compute_kl_divergence(
next_element.server_model, next_element.trained_model)
weight = postprocess_divergence(kl_div)
new_numerator = partial_accumulate.numerator + weight * next_element.trained_model
new_denominator = partial_accumulate.denominator + weight
return collections.OrderedDict(
numerator=new_numerator, denominator=new_denominator)
Putting them together
The basic outline of a round will be similar to the above; but we have put more computation 'in the stream', and consequently there wil be less on the clients. We assume here the same variable definitions.
#tff.federated_computation(...)
def round_function(...):
...
trained_clients = tff.federated_map(training_fn, clients_placed_arguments)
global_model_at_clients = tff.federated_broadcast(server_model)
# This zip I believe is not necessary, but it helps my mental model.
reduction_arg = tff.federated_zip(
collections.OrderedDict(server_model=global_model_at_clients,
trained_model=trained_clients))
# We assume a zero as specified above
return tff.federated_reduce(reduction_arg,
zero,
reduction)
I am trying to minimize x*x with adagrad optimiser. I expect to get x=0 as result, but I get value x, close to initial value.
import tensorflow as tf
x=tf.Variable(-2.)
sq=x*x
o = tf.train.AdamOptimizer(1e-1).minimize(sq)
with tf.Session() as sess:
init = tf.global_variables_initializer()
sess.run([init])
sess.run([o])
r=sess.run([x])
print("done",r)
I get -1.9 as a result, instead of expected 0.
Do I understand correctly that -2 is initial value here, or is it something else? Does AdamOptimiser perform just one step or is it possible to launch it for continious optimisation? How do I get x=0 as result?
sess.run([0]) runs only a single step. To perform a full optimization, you need to run many steps, which can be done by repeating the single step in a loop.
Thus, you can replace sess.run([o]) with:
for i in range(1000):
sess.run([o])
This yields the results 3.4735016e-23, very close to the expected 0.
In my experience, people usually run many optimization steps just as I demonstrated, with a for loop. If you are interested in implementing the loop as a TensorFlow operation, and then running this operation only once, this can be done, but it is not recommended. The reasons are: (a) I don't think you will gain any "elegance" in your code by doing this. (b) If you want to run 1000 steps, you will need to add 1000 sets of operations to your graph, and group them as one. Contrast this to needing only one set of operations.
You can see more relevant information in this question.
I could not find documentation regarding the aggregation method in tensorflow optimizer
I have the following line of code
train_op = optimizer.minimize(loss, global_step=batch, aggregation_method = tf.AggregationMethod.EXPERIMENTAL_TREE)
However, this property can be changed to be
tf.AggregationMethod.EXPERIMENTAL_ACCUMULATE_N
Does anyone know what does it do? (I just know that when I used the default with an LSTM it did not have enough memory to run)
For AggregationMethod, EXPERIMENTAL_ACCUMULATE_N is to ADD_N (DEFAULT) as accumulate_n is to add_n. add_n waits for all of its arguments to be available before doing any summation, while accumulate_n sums as soon as its inputs are available. This may save memory, but has some picky shape information limitations because its current implementation requires creating a temporary variable.
There is a bit of documentation in the comments:
# The benefit of using AccumulateN is that its inputs can be combined
# in any order and this can allow the expression to be evaluated with
# a smaller memory footprint. When used with gpu_allocator_retry,
# it is possible to compute a sum of terms which are much larger than
# total GPU memory.
# AccumulateN can currently only be used if we know the shape for
# an accumulator variable. If this is not known, or if we only have
# 2 grads then we fall through to the "tree" case below.
Question: What is the most efficient way to get the delta of my weights in the most efficient way in a TensorFlow network?
Background: I've got the operators hooked up as follows (thanks to this SO question):
self.cost = `the rest of the network`
self.rmsprop = tf.train.RMSPropOptimizer(lr,rms_decay,0.0,rms_eps)
self.comp_grads = self.rmsprop.compute_gradients(self.cost)
self.grad_placeholder = [(tf.placeholder("float", shape=grad[1].get_shape(), name="grad_placeholder"), grad[1]) for grad in self.comp_grads]
self.apply_grads = self.rmsprop.apply_gradients(self.grad_placeholder)
Now, to feed in information, I run the following:
feed_dict = `training variables`
grad_vals = self.sess.run([grad[0] for grad in self.comp_grads], feed_dict=feed_dict)
feed_dict2 = `feed_dict plus gradient values added to self.grad_placeholder`
self.sess.run(self.apply_grads, feed_dict=feed_dict2)
The command of run(self.apply_grads) will update the network weights, but when I compute the differences in the starting and ending weights (run(self.w1)), those numbers are different than what is stored in grad_vals[0]. I figure this is because the RMSPropOptimizer does more to the raw gradients, but I'm not sure what, or where to find out what it does.
So back to the question: How do I get the delta on my weights in the most efficient way? Am I stuck running self.w1.eval(sess) multiple times to get the weights and calc the difference? Is there something that I'm missing with the tf.RMSPropOptimizer function.
Thanks!
RMSprop does not subtract the gradient from the parameters but use more complicated formula involving a combination of:
a momentum, if the corresponding parameter is not 0
a gradient step, rescaled non uniformly (on each coordinate) by the square root of the squared average of the gradient.
For more information you can refer to these slides or this recent paper.
The delta is first computed in memory by tensorflow in the slot variable 'momentum' and then the variable is updated (see the C++ operator).
Thus, you should be able to access it and construct a delta node with delta_w1 = self.rmsprop.get_slot(self.w1, 'momentum'). (I have not tried it yet.)
You can add the weights to the list of things to fetch each run call. Then you can compute the deltas outside of TensorFlow since you will have the iterates. This should be reasonably efficient, although it might incur an extra elementwise difference, but to avoid that you might have to hack around in the guts of the optimizer and find where it puts the update before it applies it and fetch that each step. Fetching the weights each call shouldn't do wasteful extra evaluations of part of the graph at least.
RMSProp does complicated scaling of the learning rate for each weight. Basically it divides the learning rate for a weight by a running average of the magnitudes of recent gradients of that weight.
Suppose we have weights
x = tf.Variable(np.random.random((5,10)))
cost = ...
And we use the GD optimizer:
upds = tf.train.GradientDescentOptimizer(lr).minimize(cost)
session.run(upds)
How can we implement for example non-negativity on weights?
I tried clipping them:
upds = tf.train.GradientDescentOptimizer(lr).minimize(cost)
session.run(upds)
session.run(tf.assign(x, tf.clip_by_value(x, 0, np.infty)))
But this slows down my training by a factor of 50.
Does anybody know a good way to implement such constraints on the weights in TensorFlow?
P.S.: in the equivalent Theano algorithm, I had
T.clip(x, 0, np.infty)
and it ran smoothly.
You can take the Lagrangian approach and simply add a penalty for features of the variable you don't want.
e.g. To encourage theta to be non-negative, you could add the following to the optimizer's objective function.
added_loss = -tf.minimum( tf.reduce_min(theta),0)
If any theta are negative, then add2loss will be positive, otherwise zero. Scaling that to a meaningful value is left as an exercise to the reader. Scaling too little will not exert enough pressure. Too much may make things unstable.
As of TensorFlow 1.4, there is a new argument to tf.get_variable that allows to pass a constraint function that is applied after the update of the optimizer. Here is an example that enforces a non-negativity constraint:
with tf.variable_scope("MyScope"):
v1 = tf.get_variable("v1", …, constraint=lambda x: tf.clip_by_value(x, 0, np.infty))
constraint: An optional projection function to be applied to the
variable
after being updated by an Optimizer (e.g. used to implement norm
constraints or value constraints for layer weights). The function must
take as input the unprojected Tensor representing the value of the
variable and return the Tensor for the projected value
(which must have the same shape). Constraints are not safe to
use when doing asynchronous distributed training.
By running
sess.run(tf.assign(x, tf.clip_by_value(x, 0, np.infty)))
you are consistently adding nodes to the graph and making it slower and slower.
Actually you may just define a clip_op when building the graph and run it each time after updating the weights:
# build the graph
x = tf.Variable(np.random.random((5,10)))
loss = ...
train_op = tf.train.GradientDescentOptimizer(lr).minimize(loss)
clip_op = tf.assign(x, tf.clip(x, 0, np.infty))
# train
sess.run(train_op)
sess.run(clip_op)
I recently had this problem as well. I discovered that you can import keras which has nice weight constraint functions as use them directly in the kernen constraint in tensorflow. Here is an example of my code. You can do similar things with kernel regularizer
from keras.constraints import non_neg
conv1 = tf.layers.conv2d(
inputs=features['x'],
filters=32,
kernel_size=[5,5],
strides = 2,
padding='valid',
activation=tf.nn.relu,
kernel_regularizer=None,
kernel_constraint=non_neg(),
use_bias=False)
There is a practical solution: Your cost function can be written by you, to put high cost onto negative weights. I did this in a matrix factorization model in TensorFlow with python, and it worked well enough. Right? I mean it's obvious. But nobody else mentioned it so here you go. EDIT: I just saw that Mark Borderding also gave another loss and cost-based solution implementation before I did.
And if "the best way" is wanted, as the OP asked, what then? Well "best" might actually be application-specific, in which case you'd need to try a few different ways with your dataset and consider your application requirements.
Here is working code for increasing the cost for unwanted negative solution variables:
cost = tf.reduce_sum(keep_loss) + Lambda * reg # Cost = sum of losses for training set, except missing data.
if prefer_nonneg: # Optionally increase cost for negative values in rhat, if you want that.
negs_indices = tf.where(rhat < tf.constant(0.0))
neg_vals = tf.gather_nd(rhat, negs_indices)
cost += 2. * tf.reduce_sum(tf.abs(neg_vals)) # 2 is a magic number (empirical parameter)
You are free to use my code but please give me some credit if you choose to use it. Give a link to this answer on stackoverflow.com please.
This design would be considered a soft constraint, because you can still get negative weights, if you let it, depending on your cost definition.
It seems that constraint= is also available in TF v1.4+ as a parameter to tf.get_variable(), where you can pass a function like tf.clip_by_value. This seems like another soft constraint, not hard constraint, in my opinion, because it depends on your function to work well or not. It also might be slow, as the other answerer tried the same function and reported it was slow to converge, although they didn't use the constraint= parameter to do this. I don't see any reason why one would be any faster than the other since they both use the same clipping approach. So if you use the constraint= parameter then you should expect slow convergence in the context of the original poster's application.
It would be nicer if also TF provided true hard constraints to the API, and let TF figure out how to both implement that as well as make it efficient on the back end. I mean, I have seen this done in linear programming solvers already for a long time. The application declares a constraint, and the back end makes it happen.