What do you mean the Fed wants to increase inflation? Inflation is just a term for the state of the economy, not something the Fed can change directly... Inflation just means that the price-to-value ratio has just increased in the market. And the P::V can be for any commodity, whether it be a consumable good, a service, or even wage increases. The Fed can pump more money into the economy and thereby it will probably have an inflationary pressure to increase prices, but it doesn't necessarily mean that that is what will happen.
And the problem with COLAs is that they need to estimate how inflation will increase. Sometimes a COLA is set at the time the bill was written to, say, 5% a year, regardless of what the actual inflationary rate increase was. When the government does this, they tend to predict a little more on the high side, since (they feel) it'd be worse to not have adjusted enough and have people suffer. But what happens is that overspending on COLA means that the government is paying out more than it is collecting. The amount of money is also effected by inflation; the higher the inflation, the more goods cost (and hence the more sales taxes are collect for each unit of good sold) and the higher people's incomes are (as people get paid more for inflationary wages, the more income taxes are collected). But if a COLA is set for 5% and the inflationary rate only increases by 2%, the government has to pay out more for the adjustments than the inflationary amount of taxes were collected. Thus if the government is looking to save money, they'll be more conservative on what rate to increase COLA payments to, and during times when inflation is negligible like it is now (believe it or not, inflation rate is currently only around 1%) the government may just decide to freeze COLA increases until the inflationary rate starts to rise again.
I think inflation is a very bad move, since it really hurts people on a fixed income the most. When inflation starts to spiral higher, people's wages tend to increase to keep pace with the inflationary prices of goods and services. But people of fixed income (eg those that have retired and are living off of their savings along with the unemployed) won't get that increase in pay, and will therefore end up spending more for the same items.