Questions tagged [constrained-optimization]

For questions that involve constrained optimization problems (in the context of artificial intelligence).

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What would be a good optimization technique for this kind of problem?

Problem Description: Since I am not sure if there is a scientific term that categorizes this problem, I will do my best to describe it thoroughly. Suppose there is a chamber that's being filled with ...
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15 views

Can I add components which make the solution infeasible in Ant Colony Optimization?

While building the solution in ACO, can I add components which make the solution infeasible? I am building my algorithm based on this:
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41 views

For simple weight constraints: Add constraint directly or use parameterization without constraint

I am wondering if it makes sense to parameterize simple weight inequalities, for example if the weights should be $w\geq 0$, one cound train $\exp w$ over the unconstrained set instead. Also, if $\sum ...
2 votes
0 answers
26 views

How to create a loss function that penalizes duplicate indices in the output tensor?

We're working on a sequence-to-sequence problem using pytorch, and are using cross-entropy to calculate the loss when comparing the output sequence to the target sequence. This works fine and ...
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11 views

Stopping criteria for SMO when no solution exists for Hard Margin SVM

When we solve the dual problem using SMO, we pick two $\mu_i$'s at a time and optimize the dual wrt them while satisfying the required constraints. But in case we are using the no slack formulation of ...
0 votes
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28 views

How can TRPO with constrained form allow larger update step?

There are two optimization forms of TRPO. One is that: \begin{equation}\max\limits_{\theta}[L_{\theta_{old}}(\theta) - CD^{max}_{KL}(\theta_{old}, \theta)]\end{equation} where $C = \frac{4\epsilon\...
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0 answers
29 views

Incorporate specific constraints while training a (Conditional) variational autoencoder

I'm wondering how could I incorporate specific constraints during the training phase of a deep learning model. In particular, I work for a materials-science related project where I feed to my models ...
0 votes
0 answers
77 views

How to assign tasks to users with ranking?

I'm trying to write an automatic assignment algorithm for the following problem: I have $N$ tasks and $M$ users. For each task, I have a ranking for each user for "how related it is to that user&...
4 votes
1 answer
153 views

Which neural network can I use to solve this constrained optimisation problem?

Let $\mathcal{S}$ be the training data set, where each input $u^i \in \mathcal{S}$ has $d$ features. I want to design an ANN so that the cost function below is minimized (the sum of the square of ...
2 votes
1 answer
180 views

Intuition behind $1-\gamma$ and $\frac{1}{1-\gamma}$ for calculating discounted future state distribution and discounted reward

In the appendix of the Constrained Policy Optimization (CPO) paper (Arxiv), the authors denote the discounted future state distribution $d^\pi$ as: $$d^\pi(s) = (1-\gamma) \sum_{t=0}^\infty{\gamma^t P(...
3 votes
1 answer
446 views

How to use DQN when the action space can be different at different time steps?

I would like to employ DQN to solve a constrained MDP problem. The problem has constraints on action space. At different time steps till the end, the available actions are different. It has different ...
2 votes
2 answers
226 views

How can we design the mutation and crossover operations when the order of the genes in the chromosomes matters?

Consider an optimization problem that involves a set of tasks $T = \{1,2,3,4,5\}$, where the goal is to find a certain order of these tasks. I would like to solve this problem with a genetic algorithm,...
9 votes
1 answer
141 views

Given a list of integers $\{c_1, \dots, c_N \}$, how do I find an integer $D$ that minimizes the sum of remainders $\sum_i c_i \text{ mod } D$?

I have a set of fixed integers $S = \{c_1, \dots, c_N \}$. I want to find a single integer $D$, greater than a certain threshold $T$, i.e. $D > T \geq 0$, that divides each $c_i$ and leaves ...
1 vote
0 answers
26 views

Wasserstein GAN with non-negative weights in the critic

I want to train a WGAN where the convolution layers in the critic are only allowed to have non-negative weights (for a technical reason). The biases, nonetheless, can take both +/- values. There is no ...
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2 votes
2 answers
84 views

How does one make a neural network learn the training data while also forcing it to represent some known structure?

In general, how does one make a neural network learn the training data while also forcing it to represent some known structure (e.g., representing a family of functions)? The neural network might find ...
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2 votes
1 answer
217 views

How to handle infeasibility caused due to crossover and mutation in genetic algorithm for optimization?

I have chromosomes with floating-point representation with values between $0$ and $1$. For example Let $p_1 = [0.1, 0.2, 0.3]$ and $p_2 = [0.5, 0.6, 0.7]$ be two parents. Both comply with the set of ...
4 votes
2 answers
1k views

How do we design a neural network such that the $L_1$ norm of the outputs is less than or equal to 1?

What are some ways to design a neural network with the restriction that the $L_1$ norm of the output values must be less than or equal to 1? In particular, how would I go about performing back-...
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3 votes
2 answers
999 views

How to use a VAE to reconstruct an image starting from an initial image instead of starting from a random vector?

Is it possible to use a VAE to reconstruct an image starting from an initial image instead of using K.random_normal, as shown in the “sampling” function of this ...