fts_solver/impls/

clarabel.rs

use crate::{AuctionOutcome, HashMap, PortfolioOutcome, ProductOutcome, Solver, Submission};
use clarabel::{algebra::*, solver::*};
use std::hash::Hash;

/// A solver implementation that uses the Clarabel interior point method
/// for quadratic programming to solve the market clearing problem.
///
/// This solver is generally more accurate but can be slower than ADMM-based
/// solvers for large problems. It's a good choice when high precision is needed.
pub struct ClarabelSolver(DefaultSettings<f64>);

impl Default for ClarabelSolver {
    fn default() -> Self {
        let mut settings = DefaultSettings::default();
        settings.verbose = false;
        Self(settings)
    }
}

impl Solver for ClarabelSolver {
    type Settings = DefaultSettings<f64>;

    fn new(settings: Self::Settings) -> Self {
        Self(settings)
    }

    fn solve<
        T,
        BidderId: Eq + Hash + Clone + Ord,
        PortfolioId: Eq + Hash + Clone + Ord,
        ProductId: Eq + Hash + Clone + Ord,
    >(
        &self,
        auction: &T,
        // TODO: warm-starts with the prices
    ) -> AuctionOutcome<BidderId, PortfolioId, ProductId>
    where
        for<'t> &'t T: IntoIterator<Item = (&'t BidderId, &'t Submission<PortfolioId, ProductId>)>,
    {
        let (products, ncosts) = super::prepare(auction);

        if products.len() == 0 {
            return AuctionOutcome::default();
        }

        // The trade and bid constraints are all (something) = 0, we need to
        // know how many of these there are in order to handle the box
        // constraints for each decision variable
        let nzero = products.len() + ncosts;

        // Our quadratic term is diagonal, so we build the matrix by defining its diagonal
        let mut p = Vec::new();
        // and these are the linear terms
        let mut q = Vec::new();

        // Clarabel handles constraints via a cone specification, e.g. Ax + s = b, where s is a cone.
        // The first `nzero` of b and s are just =0, so we do that work upfront.
        let mut b = vec![0.0; nzero];
        let mut s = vec![ZeroConeT(nzero)];

        // Clarabel's matrix input is in the form of CSC, so we handle the memory representation
        // carefully.
        let mut a_nzval = Vec::new();
        let mut a_rowval = Vec::new();
        let mut a_colptr = Vec::new();

        // These will help us figure out the correct row index as we iterate.
        let mut group_offset = products.len();

        // We begin by setting up the portfolio variables
        for (_, submission) in auction.into_iter() {
            for (id, portfolio) in submission.portfolios.iter() {
                // portfolio variables contribute nothing to the objective
                p.push(0.0);
                q.push(0.0);

                // start a new column in the constraint matrix
                a_colptr.push(a_nzval.len());

                // We copy the portfolio definition into the matrix
                for (product, &weight) in portfolio.iter() {
                    a_nzval.push(weight);
                    a_rowval.push(products.get_index_of(product).unwrap());
                }

                // Now we embed the weights from each group. This loop is a little wonky;
                // in matrix terms, the representation is transposed in the wrong way.
                // However, we expect the number of groups to be fairly small, so simply
                // searching every group for every portfolio in the submission is not so bad.
                for (offset, (group, _)) in submission.demand_curves.iter().enumerate() {
                    if let Some(&weight) = group.get(id) {
                        a_nzval.push(weight);
                        a_rowval.push(group_offset + offset);
                    }
                }
            }

            group_offset += submission.demand_curves.len();
        }

        // Now we setup the segment variables
        group_offset = products.len();
        for (_, submission) in auction.into_iter() {
            for (_, curve) in submission.demand_curves.iter() {
                for segment in curve.iter() {
                    let (m, pzero) = segment.slope_intercept();

                    // Setup the contributions to the objective
                    p.push(-m);
                    q.push(-pzero);

                    // Insert a new column
                    a_colptr.push(a_nzval.len());

                    // Ensure it counts towards the group
                    a_nzval.push(-1.0);
                    a_rowval.push(group_offset);

                    // Setup the box constraints
                    // x0 <= y <= x1 ==> -y + s == -x0 and y + s == x1
                    if segment.q0.is_finite() {
                        a_nzval.push(-1.0);
                        a_rowval.push(b.len());
                        b.push(-segment.q0);
                    }
                    if segment.q1.is_finite() {
                        a_nzval.push(1.0);
                        a_rowval.push(b.len());
                        b.push(segment.q1);
                    }
                }

                // Advance the group offset for the next bid/constraint
                group_offset += 1;
            }
        }

        // We need to polish off the CSC matrix
        a_colptr.push(a_nzval.len());

        let a_matrix = CscMatrix {
            m: b.len(),
            n: p.len(),
            colptr: a_colptr,
            rowval: a_rowval,
            nzval: a_nzval,
        };

        assert!(a_matrix.check_format().is_ok()); // TODO: maybe remove this

        // We also need to cleanup the cone specification
        s.push(NonnegativeConeT(b.len() - nzero));

        // Finally, we need to convert our p spec into a csc matrix
        let p_matrix = {
            let m = p.len();
            let n = p.len();

            CscMatrix {
                m,
                n,
                colptr: (0..=n).collect(),
                rowval: (0..n).collect(),
                nzval: p,
            }
        };

        // Now we can solve!
        let mut solver = DefaultSolver::new(&p_matrix, &q, &a_matrix, &b, &s, self.0.clone());
        solver.solve();
        assert_eq!(solver.solution.status, SolverStatus::Solved);

        // We get the raw optimization output

        let mut product_outcomes: HashMap<ProductId, ProductOutcome> = products
            .into_iter()
            .zip(solver.solution.z.iter())
            .map(|(product, &price)| (product, ProductOutcome { price, trade: 0.0 }))
            .collect();

        let mut trades = solver.solution.x.iter();

        let submission_outcomes = auction
            .into_iter()
            .map(|(bidder_id, submission)| {
                let outcome = submission
                    .portfolios
                    .iter()
                    .map(|(id, portfolio)| {
                        // Safe, because we necessarily have every portfolio represented in the solution
                        let trade = *trades.next().unwrap();

                        let mut price = 0.0;

                        for (product_id, weight) in portfolio.iter() {
                            // Safe, because product outcomes contains all referenced products
                            let product_outcome = product_outcomes.get_mut(product_id).unwrap();

                            // We report the trade (in an absolute sense), to be halved later
                            product_outcome.trade += (weight * trade).abs();

                            // We also compute the effective price of the portfolio
                            price += weight * product_outcome.price;

                            // TODO: consider special summation algorithms (i.e. Kahan) for the above dot products
                        }

                        (id.clone(), PortfolioOutcome { price, trade })
                    })
                    .collect::<HashMap<_, _>>();

                (bidder_id.clone(), outcome)
            })
            .collect::<HashMap<_, _>>();

        // We have double-counted the trade for each product, so we halve it
        for outcome in product_outcomes.values_mut() {
            outcome.trade *= 0.5;
        }

        // TODO:
        // We have assigned the products prices straight from the solver
        // (and computed the portfolio prices from those).
        // Under pathological circumstances, the price may not be unique
        // (either when there is no trade, or the supply exactly matches the demand).
        // We should think about injecting an auxiliary solve for choosing a canonical
        // price and/or for detecting when there is such a degeneracy.

        // TODO:
        // When there are "flat" demand curves, it is possible for nonuniqueness
        // in the traded outcomes. The convex regularization is to minimize the L2 norm
        // of the trades as a tie-break. We should think about the best way to regularize
        // the solve accordingly.

        AuctionOutcome {
            submissions: submission_outcomes,
            products: product_outcomes,
        }
    }
}