  Combinatorial Optimization is crucial to numerous real-world applications,
yet still presents challenges due to its (NP-)hard nature. Amongst existing
approaches, heuristics often offer the best trade-off between quality and
scalability, making them suitable for industrial use. While Reinforcement
Learning (RL) offers a flexible framework for designing heuristics, its
adoption over handcrafted heuristics remains incomplete within industrial
solvers. Existing learned methods still lack the ability to adapt to specific
instances and fully leverage the available computational budget. The current
best methods either rely on a collection of pre-trained policies, or on
data-inefficient fine-tuning; hence failing to fully utilize newly available
information within the constraints of the budget. In response, we present
MEMENTO, an RL approach that leverages memory to improve the adaptation of
neural solvers at inference time. MEMENTO enables updating the action
distribution dynamically based on the outcome of previous decisions. We
validate its effectiveness on benchmark problems, in particular Traveling
Salesman and Capacitated Vehicle Routing, demonstrating it can successfully be
combined with standard methods to boost their performance under a given budget,
both in and out-of-distribution, improving their performance on all 12
evaluated tasks.
