CODEWITHSUNDEEP
pythoncvxpyconvex-optimizationconvex
evrihikri
evrihikri

Reputation: 1

Optimization problem: cvxpy returns that the problem is not DPP

I am writing a convex optimization problem with cvxpy, but it returns that the problem is not DPP even though it is.

import cvxpy as cp
import numpy as np
from cvxpylayers.tensorflow import CvxpyLayer

# Simplified proxy functions for debugging
def score(x, w, b):
    return x @ w + b

def sign_proxy(x, w, b, temperature=1):
    return 0.5 * cp.norm(cp.hstack([1, (temperature * score(x, w, b) + 1)]), 2) + \
           0.5 * cp.norm(cp.hstack([1, (temperature * score(x, w, b) - 1)]), 2)

def c_Quad(x, xt, scale=1):
    return scale * cp.sum_squares(x - xt)

class DELTA:
    def __init__(self, x_dim, N, funcs):
        self.score_fn = funcs["score_fn"]
        self.cost_fn = funcs["cost_fn"]
        self.sign_proxy_fn = funcs["sign_proxy_fn"]
        
        self.xt = cp.Variable(x_dim)
        self.x = cp.Parameter(x_dim)
        self.w = cp.Parameter((x_dim, N))
        self.b = cp.Parameter(N)
        
        sign_proxy = self.sign_proxy_fn(self.xt, self.w, self.b)
        target = cp.sum(sign_proxy) - self.cost_fn(self.xt, self.x)
        
        X_LOWER_BOUND = -10  # Example value, replace with your actual lower bound
        X_UPPER_BOUND = 10   # Example value, replace with your actual upper bound
        constraints = [
            self.xt >= X_LOWER_BOUND,
            self.xt <= X_UPPER_BOUND
        ]
        
        objective = cp.Maximize(target)
        problem = cp.Problem(objective, constraints)
        print(problem.is_dcp(dpp=True))
        
        self.layer = CvxpyLayer(problem, parameters=[self.x, self.w, self.b], variables=[self.xt])
        
    def optimize_X(self, x, w, b):
        return self.layer(x, w, b)[0]

# Example usage
x_dim = 5  # Example dimension
N = 10  # Example number of columns

funcs = {
    "score_fn": score,
    "cost_fn": c_Quad,
    "sign_proxy_fn": sign_proxy
}

delta = DELTA(x_dim, N, funcs)
x = np.random.randn(x_dim)
w = np.random.randn(x_dim, N)
b = np.random.randn(N)

# Optimize X
optimized_xt = delta.optimize_X(x, w, b)
print("Optimized xt:", optimized_xt)

The line:

self.layer = CvxpyLayer(problem, parameters=[self.x, self.w, self.b], variables=[self.xt])

fails on "Problem must be DPP": ValueError: Problem must be DPP. even though all the elements in the problem are convex. What do I need to do?

Upvotes: 0

Views: 102

Answers (1)

Iakl
Iakl

Reputation: 23

I think that your problem is not DCP, and therefore not DPP.

My guess is that in this line:

target = cp.sum(sign_proxy) - self.cost_fn(self.xt, self.x)

you are negating a concave function and therefore making it convex and then you are trying to maximize it. Please tell me if I'm wrong.

Maybe you should take a look at the signs?

Upvotes: 0

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