Lambda key comparator for map

I'm trying to implement my own key comparator for std::map as follows:

auto cost_compare = [](const OffsetCoords& left, const OffsetCoords& right) { 
return (left == right); };

std::map<OffsetCoords, int, decltype(cost_compare)> cost_so_far(cost_compare);

where OffsetCoords is struct, vector of x, y values with overloaded operator==

code builds fine, but when I call cost_so_far.count(some_offsetcoords_variable) it throws exception 'Expression: invalid comparator'.

What's the proper way to do this?