If your lease clearly states they are responsible, send them a certified letter explaining the problem and request they correct it. You can purchase a return receipt at the time of mailing or you can purchase it after mailing for a bit higher cost. Keep a copy of the letter as well. This return receipt and your letter copy will be your proof that you notified them of a problem. Most states allow landlords a 30 day period from being notified to correct an issue. Some states may be more strict or less strict, check your local laws and your lease for specifics. You could also write your notice on your rent check and request a copy of the cancelled check once it clears your bank to show that you gave them written notice and they received it (since they cashed your check to their bank account).
If you have no response after the time limit, ask your landlord if he will agree to mutually rescind the lease. I'd recommend doing this with another certified letter. If they decline or you still have no response, it may be possible to break your lease by filing in court for a breach of contract (your lease). You should always check your local laws before doing this. It usually can't hurt to ask the court clerk about it or an attorney. If you end up going through the court process and have proper evidence that you notified your landlord (Your certified mail receipts with the the landlord's signatures are good), you should be able to work out some kind of arrangement with your landlord in the court room/on public record. It's also possible that they could resist and the entire ordeal could take a long time or cost a lot of money as well.
Some alternatives would be to send the initial request letter, and if no response, contact a local health agency or other third party. The only problem is they may "condemn" the home if they feel it's bad enough forcing you to leave almost immediately.
You could also send the request and say if you have no response you'll take care of the issue and bill them (or something) and then after the time limit, hire your own pest control company or use a DIY method (bug bombs are pretty cheap). You would then have to collect from your landlord afterward. It would be hard to collect on any amount that was considered "unreasonable".
I would NOT recommend withholding any amount from your rent as your landlord could file for eviction for any missing rent if they wanted (most won't for low amounts but some do). If your landlord offers you a credit on your rent for doing it, be sure to get it in writing before deducting anything.
In my opinion, the easiest method would be to write the letter to your landlord, but treat the problem yourself. Boric acid (Borax powder, laundry aisle) is extremely effective if used properly and fairly inexpensive and easy to use without risking contamination to your food or yourself. These treatments along with strict cleaning of everything and removing sources of food and water (leaking pipes/basements or standing water after a shower or running the sink) for the bugs can help a ton as well. You can also buy baits that are easy to use, safe, effective if used properly, and not too expensive.