Questions tagged [constrained-optimization]
For questions that involve constrained optimization problems (in the context of artificial intelligence).
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Can we derive the support vector machines dual formulation without directly using lagrangian duality theory?
Lagrangian duality theory allows us to derive the dual formulation for support vector machines and to show that the primal and the dual solutions are equivalent.
My question is: is it possible to ...
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Inquiry about utilising AI in CNC machining path generation
I will begin by describing a situation. I work in laser machining control company. The essence of the problem, to which I would like to try to apply AI based tool is this:
Say I have a analytically ...
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Intuition behind replacing constraint in equation for Optimal Separating Hyperplane
I am reading "Optimal Separating Hyperplane" section of the book - Elements of Statistical Learning which is described on page 132 as follows:
My questions:
The constraint $||\beta|| = 1$ ...
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Why do Soft Actor-Critic with automatic temperature tuning use only a single dual variable?
In section 5 of the paper “Soft Actor Critic Algorithms and Applications”, the authors propose to optimize the policy subject to the constraints that the entropy of action distribution should be ...
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Constrain or not constrain overlapping architectural choices when wanting to compare deep neural architectures
I want to compare various deep (recurrent) neural architectures and was wondering what the best approach is. The models in question all use several LSTMs/GRUs etc.
Fine-tune all models fully and ...
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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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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 ...
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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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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&...
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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 ...
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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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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 ...
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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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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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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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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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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 ...
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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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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 ...
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