Questions tagged [constrained-optimization]

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

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How to constrain some actions in a multi-dimensional action space?

In portfolio management (allocation) the action space is given by the weights of the assets, i.e. $\sum_{i=1}^m a_i=1$. There may be some weight constraints like one cannot allocate more than 10% of ...
2
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1answer
64 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(...
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44 views

How can I model this problem as optimization problem that can be solved with ACO?

I have the following homework problem, where I need to explain how to model a certain problem as an optimization problem and how I can solve it with ACO. You have 6 portable media players $(P_i, ...
3
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1answer
129 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
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2answers
129 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,...
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0answers
99 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 ...
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0answers
23 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 ...
2
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1answer
85 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 ...
6
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2answers
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-...
3
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2answers
557 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 ...